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f21fe5887d557a228fd28824d2a54744d1ff296f
subsection
20
130
Body
According to the relation (REF ) between the tension and the vector, the tension associated with a fundamental weight \lambda ^1 is \mathcal {T}_1=R_1/l_p^3 . This is the tension of a string in the external d-dimensional spacetime. More concretely, this string can be interpreted as an M2-brane wrapped along the interna...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.004925128538161516, 0.00748878950253129, -0.03329707309603691, -0.009995225816965103, -0.006939433515071869, -0.019608953967690468, 0.006535046733915806, -0.010391983203589916, 0.013718638569116592, 0.022721972316503525, -0.005176916718482971, 0.02696421928703785, -0.010689551010727882, ...
f4b9e555ffa645746aaf78d685b35361d2d9abef
subsection
21
130
Body
The tension is given by T^{(\text{\tiny KKM})}_5=R_1^2R_2/l_p^9 and it corresponds to \lambda ^{(\text{\tiny KKM})}=\lambda _1 + \lambda _2 . Namely, the second 5-brane multiplet has the Dynkin label [1,1,0,\cdots ,0]. Higher p-brane multiplets can also be constructed similarly. We can summarize this subsection with Ta...
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10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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8948bc802bbe9575d9c6993f09e1a5bb338d67de
subsection
22
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Body
Again by performing a formal T-duality along the x^8-direction, we obtain the background of the 5^3_2(12345,678)-brane,{\mathrm {d}}s^2 = {\mathrm {d}}x^2_{01\cdots 5} + \frac{\tau _2}{\vert {\tau } \vert ^2} \, {\mathrm {d}}x^2_{67} + \tau _2^{-1} \,{\mathrm {d}}x_{8}^2 + \tau _2 \,{\mathrm {d}}x_{9}^2\,,\quad \operat...
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10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.04936489462852478, 0.01534644141793251, -0.04076112434267998, -0.023873936384916306, -0.017741462215781212, -0.016902443021535873, 0.007593132555484772, 0.008611397817730904, 0.037405043840408325, 0.029777588322758675, -0.049120817333459854, -0.003331291489303112, -0.02230268158018589, ...
5387ee206ba574fdf4899ff5f0cbb583af52819d
subsection
23
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Body
More explicitly, we obtainLet us note that this map can be singular in certain backgrounds, for example, when E_{mn} is not invertible.\begin{split} &\tilde{g}_{mn} = E_{mp}\,E_{nq}\,g^{pq}\,,\qquad \beta ^{mn} = E^{mp}\,E^{nq}\,B_{pq}\,,\qquad \operatorname{e}^{-2\tilde{\phi }} \equiv \frac{\det (g_{mn})}{\det (E_{mn}...
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10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.07090054452419281, 0.014712473377585411, -0.0353892557322979, -0.01755734346807003, -0.0064715053886175156, -0.028616486117243767, 0.005087205674499273, 0.07193781435489655, 0.023353859782218933, 0.033131666481494904, -0.045700956135988235, -0.016184484586119652, 0.014148076064884663, 0...
d7c0874078f690345d8fcaa483261805293661aa
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Body
In fact, as we show in the next section, in all of the “elementary” domain-wall solutions, the winding-coordinate dependence appears only in a certain gauge field linearly.With the above parameterization, the linear map (REF ) (a T-duality along the y-direction) between the generalized coordinates can be summarized as ...
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10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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c2add1306fc11a822022cf5b22728c9f2c46e672
subsection
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Body
However, even if a minus sign can appear, it does not affect the following computations for obtaining exotic-brane solutions in EFT since the minus sign can be absorbed into a free parameter m .&x^a\ \leftrightarrow \ x^a\,,\qquad \tilde{x}_a\ \leftrightarrow \ \tilde{x}_a\,,\qquad x^y\ \leftrightarrow \ \tilde{x}_y\,,...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ 0.023850006982684135, 0.033753179013729095, -0.03787314146757126, 0.006370683200657368, -0.006065500900149345, -0.03222726657986641, 0.0031624529510736465, -0.0011959336698055267, 0.0332648865878582, 0.022522464394569397, -0.024017857387661934, 0.02108810655772686, -0.003809058340266347, 0...
4779746b11e6a0b59ecd91b861b1c5cecdc95d39
subsection
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Body
The dual fields in M-theory and type IIB theory can be summarized as\text{M-theory}:\quad &\bigl \lbrace \tilde{G}_{ij},\,\Omega ^{i_1i_2i_3},\,\Omega ^{i_1\cdots i_6},\,\Omega ^{i_1\cdots i_8,\,j}\bigr \rbrace \,, \\ \text{type IIB}:\quad &\bigl \lbrace \tilde{g}_{mn},\, \tilde{\phi },\,\gamma ,\,\beta ^{mn},\, \gamma...
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10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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6d4bf6bab5eec4fe85665f221988456890c0c83f
subsection
27
130
Body
In the following, for simplicity, we drop the subscript {\text{\tiny (A)}} for the type IIA fields.In summary, the T-duality transformation (REF ) and (REF ) maps a solution of EFT to another solution of EFT. Although (REF ) is the result for the E_{7(7)} EFT , if we consider the E_{8(8)} EFT, there appears an addition...
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10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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1f080563d976041b445c5b09170d27b9f727a0bf
subsection
28
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Body
\end{split}The S-duality rule for \beta ^{m_1\cdots m_7,\,n} will be \beta ^{\prime m_1\cdots m_7,\,n}=\beta ^{m_1\cdots m_7,\,n}+\text{(non-linear terms)} .
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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fbc696928d4c48d9effcd34b3ec99b9aa614d136
subsection
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Body
The S-duality transformation also rotates the generalized coordinates as\begin{split} &\tilde{x}^{\prime }_m = - y^{\text{\tiny D}}_m\,,\quad y^{\prime \text{\tiny D}}_m = \tilde{x}_m\,,\quad y^{\prime \text{\tiny D}}_{m_1\cdots m_5} = - y^{\text{\tiny S}}_{m_1\cdots m_5}\,, \\ &y^{\prime \text{\tiny S}}_{m_1\cdots m_5...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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01b8b48d217e5c3c8f39b4d0cb9c68bfd1db755b
subsection
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Body
By performing the T-duality along the x^8-direction, we obtain the p_3^{(1,7-p)}(1\cdots p,p+1\cdots 7,8)-brane solution\begin{split} &{\mathrm {d}}s^2 = \frac{\vert {\tau } \vert }{\tau _2^{1/2}}\, \bigl ({\mathrm {d}}x^2_{01\cdots p}+\tau _2\,{\mathrm {d}}x_{9}^2\bigr ) + \frac{\tau _2^{1/2}}{\vert {\tau } \vert }\, ...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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6513a62ce9970ce8e9d7d2a8ca1f48c0e593e929
subsection
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\end{split}By performing a formal T-duality along the x^8-direction, we obtain the 1_4^{(1,0,6)}(1,234567,,8) background,{\mathrm {d}}s^2= \frac{\vert {\tau } \vert ^2}{\tau _2} \, \bigl ({\mathrm {d}}x_{01}^2 + \tau _2\,{\mathrm {d}}x_9\bigr )+ {\mathrm {d}}x^2_{2\cdots 8} \,, \quad \operatorname{e}^{-2\Phi } = \frac{...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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3ee886b373aa82e4de326e9b2fb912d07798504d
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Body
In this case, the linear winding-coordinate dependence is contained in the \beta -field \beta ^{67}=m\,\tilde{x}_8 . For generality, we introduce an arbitrary constant c and decompose the \beta -field as\beta = m\,\tilde{x}_8\,\partial _{6}\wedge \partial _7 = c\,\partial _{6}\wedge \partial _7 + \frac{1}{2}\,U^{mn}\,\...
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10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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2ea94a6a2ec5bd299e126fc51cbd5d9c2cabff1d
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In particular, when we choose c=0 , the solution is simplified as{\mathrm {d}}s^2 = {\mathrm {d}}x^2_{01\cdots 5} + \tau _2^{-1} \,{\mathrm {d}}x_{678}^2 + \tau _2 \,{\mathrm {d}}x_{9}^2\,, \qquad \operatorname{e}^{-2\Phi }= \tau _2^2 \,,where the asymmetry between \lbrace 6,7\rbrace and 8 disappears.According to the g...
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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008ed5a292dae7706179e7bee5f5d888cc6e9820
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In other words, we are essentially describing a seven-dimensional supergravity.In this manner, we have transformed the DFT solution (REF ) into a winding-coordinate-independent solution (REF ) of the deformed supergravity. In principle, we can repeat this procedure to all of the “elementary” domain-wall solutions in DF...
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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52b01c6fc42b87c8807046526dd12fff43c5f4cb
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Example: string multiplet in
As an example, let us consider a string multiplet in M-theory compactified on T^6 , where the U-duality group is E_{6(6)} . We start from the highest weight vector [1,0,0,0,0,0] that corresponds to a 2_3-brane wrapped along the x^1-direction. In order to indicate that the 2_3-brane behaves as a string in the external f...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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cb0747ab8a20615c5a99fdffafb6b70c1b17ecae
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Example: string multiplet in
It is noted that, in this case, all of the states correspond to weight vectors with the same length, and the 27 states are connected via the Weyl reflections, or the U-duality transformations (REF ).
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
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7de64f7e10a748423b920305b24b74f5ee92da2c
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Web of supersymmetric branes
Utilizing the duality transformation rule (REF ), we can generate a chain of exotic branes in M-theory. Indeed, by brute force applications of duality (REF ) to the tensions of the standard branes, we obtain Tables REF –REF , which show the explicit brane charges and the degeneracies in each multiplet. By summing up th...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
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9d5e1c1ef3cfd73f4cfcc76a67fb7fdfd3551f60
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Web of supersymmetric branes
In M-theory compactified to d-dimensions with d\ge 3, all of the branes appearing in the Weyl orbit are summarized as follows (potentials that couple to the following branes are listed in ):\begin{split} &\text{P}\,,\ 2_3\,,\ 5_6\,,\ 6_{9}^{1}\,,\ {purple}{5_{12}^{3}}\,,\ {blue}{8_{12}^{(1,0)}}\,,\ {purple}{2_{15}^{6}}...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ 0.0028313451912254095, 0.03357929736375809, 0.01363014243543148, -0.04505731165409088, -0.020269684493541718, -0.03519720956683159, 0.029519254341721535, -0.008142979815602303, 0.02890872210264206, 0.025489740073680878, -0.022101283073425293, -0.014889365993440151, -0.0026329222600907087, ...
5bcb7b7d8aaaf5f0ab4b1f1308e5e1ab6c5db11a
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Web of supersymmetric branes
\end{split}In the literature, 2_3, 5_6, 6_{9}^{1}, and 8_{12}^{(1,0)} are respectively called M2, M5, KKM, and M9-brane while the others do not have familiar common names. We consider a b_{n}^{(c_s,\cdots ,c_2)}-brane as a kind of (b+c_2+\cdots +c_s)-brane, and the codimension is given by 10-(b+c_2+\cdots +c_s). If the...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.00576135516166687, -0.0035388455726206303, -0.0395892858505249, -0.028875453397631645, -0.02402217872440815, -0.004876166582107544, 0.009393678978085518, -0.018909454345703125, -0.01669648289680481, -0.00042232449050061405, -0.03641481697559357, 0.03714738413691521, -0.037666287273168564,...
e4767a664622d4637c4c6d3893996697252a8046
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Web of supersymmetric branes
The tension is \mathcal {T}_7=R_1^3R_2/l_p^{12} , corresponding to 2\,\lambda _1 + \lambda _2 and [2,1,0] in d=8.We can also consider the type II branes by using the 11D/10D relation (REF ), and the type IIA branes associated with all of the “elementary” M-branes are obtained in Table REF . [Table: A map between branes...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 4459, "openalex_id": "", "raw": "E. Lozano-Tellechea and T. Ortín, “7-branes and higher Kaluza-Klein branes,” Nucl. Phys. B 607, 213 (2001) [hep-th/0012051].", "source_ref_id": "ebb2964e21e87eec8ca1569348c27d45c69532ae", ...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ 0.00839375052601099, 0.03272036463022232, -0.0344601608812809, -0.051339227706193924, -0.021991625428199768, -0.026341114193201065, 0.0444716140627861, 0.002560093766078353, 0.03986268490552902, 0.017443738877773285, -0.0473407506942749, -0.007279670797288418, -0.023304102942347527, 0.0107...
4e5844fd291196e8f7cac5fa8cf0aba66d54873c
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Web of supersymmetric branes
In addition, 7_{3}^{(1,0)} is known as the KK8A-brane in . As one can clearly see, in dimensions d\ge 3 , there exist the type IIA branes with tensions proportional to g_s^{\alpha } with -11\le \alpha \le 0 .In order to obtain all of the “elementary” type IIB branes, we act a T-duality to each of the type IIA branes. S...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 58, "openalex_id": "", "raw": "P. Meessen and T. Ortín, “An Sl(2,Z) multiplet of nine-dimensional type II supergravity theories,” Nucl. Phys. B 541, 195 (1999) [hep-th/9806120].", "source_ref_id": "9df00eb9eecea1a7634d6298a1...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.0016289048362523317, 0.04589925706386566, -0.033081647008657455, -0.0406196229159832, -0.034485481679439545, -0.0032539949752390385, 0.049439359456300735, -0.00019157274800818413, 0.018432946875691414, -0.014023077674210072, -0.03527894988656044, 0.016693413257598877, -0.03613345697522163...
a94aa7b1cb2f7ef33d64b3633b3dc7112d6735d4
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Web of supersymmetric branes
A list of all of the “elementary” type IIB branes is as follows:&1_0\,,\ \text{P}\,,\ 1_1\,,\ 3_1\,,\ 5_1\,,\ {purple}{7_1}\,,\ {darkcyan}{9_1}\,,\ 5_2\,,\ 5_2^1\,,\ {purple}{5_{2}^{2}}\,,\ {blue}{5_{2}^{3}}\,,\ {darkcyan}{5_{2}^{4}}\,,\ {purple}{7_{3}}\,,\ {purple}{5_{3}^{2}}\,,\ {purple}{3_{3}^{4}}\,,\ {purple}{1_{3}...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.039226558059453964, 0.016133258119225502, -0.02336804009974003, -0.020895391702651978, -0.007070701569318771, 0.0099440086632967, 0.02284908853471279, 0.0037318652030080557, 0.0049071358516812325, 0.013790348544716835, -0.018819591030478477, 0.012828763574361801, -0.01814800687134266, 0...
b9e7638154dc55e4963c382d7720526b6a966c67
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Web of supersymmetric branes
For example, 2^{(7,0,0,0)}_{11(8)} in Figure REF represents the 2^{(7,0,0,0)}_{11}-brane, and also denotes that its S-dual partner is the 2^{(7,0,0,0)}_{8}-brane. The characters in the squared brackets are not important here, and will be explained in Section REF . Each (solid or dashed) line corresponds to a T-duality ...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.03555922210216522, 0.039924003183841705, -0.033453140407800674, -0.024082597345113754, -0.02951568178832531, 0.02429625764489174, 0.011697916314005852, 0.026982277631759644, 0.022022299468517303, 0.039649296551942825, -0.03269006684422493, -0.004860777873545885, -0.035650789737701416, -...
53e1beb304b6b6fcded607eef91c406572a597fb
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Web of the missing states
In the previous subsection, we have only considered the branes that are connected to the standard branes via T- and S-duality transformations, i.e. the Weyl reflections (REF ). However, as we can clearly see from Table REF , if we consider the non-standard branes (i.e. colored branes with codimension 2 or less), these ...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 577, "openalex_id": "", "raw": "S. Elitzur, A. Giveon, D. Kutasov and E. Rabinovici, “Algebraic aspects of matrix theory on T^d,” Nucl. Phys. B 509, 122 (1998) [hep-th/9707217].", "source_ref_id": "088e9c46d5d8dad95de5769026...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.05404799431562424, 0.010383867658674717, -0.0006737879011780024, -0.0061418176628649235, -0.01643412932753563, 0.017883751541376114, 0.05276622250676155, 0.0383005253970623, 0.003978829365223646, 0.020782994106411934, -0.0026550963521003723, 0.021484917029738426, -0.030060572549700737, ...
326ac03cf8b91e2bb13d1066476044c3d1645b11
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Example: 4-brane multiplet in
Let us start with a simple example, a 4-brane multiplet in M-theory compactified on T^4. In this case, Table REF shows that the number of supersymmetric branes is 20, although the dimension of the 4-brane multiplet is 24. Thus, there are four missing states. In order to identify the missing states, let us consider the ...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 1001, "openalex_id": "", "raw": "S. Elitzur, A. Giveon, D. Kutasov and E. Rabinovici, “Algebraic aspects of matrix theory on T^d,” Nucl. Phys. B 509, 122 (1998) [hep-th/9707217].", "source_ref_id": "088e9c46d5d8dad95de576902...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.011596065945923328, 0.011962257325649261, -0.03524593636393547, -0.005378438625484705, 0.0229480043053627, -0.028913874179124832, 0.03390323370695114, 0.021773139014840126, -0.015792010352015495, 0.028166234493255615, -0.021712107583880424, -0.00503513403236866, -0.046445295214653015, 0...
26cbeb92d77dfde24c75971cd5da6e2027123a18
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List of missing states
Generalizing the above procedure, we can compute the tensions of missing states in all of the multiplets. In order to obtain a list of the weights for the exceptional groups E_{6(6)}, E_{7(7)}, and E_{8(8)}, it will be useful to use a computer program such as SimpLie . By transforming the Dynkin labels into the tension...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 269, "openalex_id": "", "raw": "T. Nutma, SimpLie, a simple program for Lie algebras, https://github.com/teake/simplie.", "source_ref_id": "ad7344b901ff360b18e9803e1e671347957384c6", "start": 106 } ] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.014884646981954575, -0.009185604751110077, -0.02751103974878788, 0.0004725360486190766, -0.004917045123875141, -0.03823775053024292, 0.06378044933080673, 0.019622405990958214, -0.033965375274419785, 0.007327884901314974, -0.022170571610331535, 0.02865542471408844, -0.03973308205604553, ...
b77032f68c7efff99d55d2f5ae24b2f263b7e6d5
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List of missing states
The states contained in a single column have the weights with the same length, and we have checked that they are indeed in a single U-duality orbit of (REF ).In terms of M-theory, the following states are contained in Tables REF –REF :&8_9\,, 7_{12}^{2}\,, 9_{12}^{1}\,, 4_{15}^{5}\,, 6_{15}^{4}\,, 7_{15}^{(1,2)}\,, 1_{...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.02253003418445587, -0.016870830208063126, -0.03935510292649269, -0.017847081646323204, -0.0265265591442585, 0.031209511682391167, 0.04444991052150726, 0.05961230397224426, -0.013728524558246136, 0.011043835431337357, -0.04451092705130577, -0.013652254827320576, 0.0035713231191039085, 0....
adfeaffa89464d658b99b0cfadcdb8f58893c631
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List of missing states
For example, the 8_9-brane in the p-brane multiplet (1\le p\le 6) has degeneracy (8-p) , although for p=6 the degeneracy becomes 1. The p-dependence is non-trivial, but the degeneracy is independent of d for all missing states. The missing states in higher d can be obtained from the missing states in lower d just by tr...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ 0.014783431775867939, -0.008032483980059624, -0.038873255252838135, -0.024715334177017212, -0.04030735418200493, -0.022976107895374298, 0.061422184109687805, 0.029994042590260506, -0.005652488674968481, -0.0016143156681209803, -0.04738631471991539, -0.010893055237829685, -0.03768325597047806...
f2c21df04951720d0e86c2d4535009429335a5bd
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Web of mixed-symmetry potentials
The standard branes in type II theory couple to certain potentials in type II supergravity. For example, the F1 and the pp-wave (electrically) couple to the B-field B_2 and the graviphoton A_1^m , and Dp-branes couple to the R–R potentials C_{p+1} . Following a series of works , , , , , , , , , , we call F1 and the pp-...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep11(2010)139", "end": 350, "openalex_id": "https://openalex.org/W3102269067", "raw": "E. A. Bergshoeff and F. Riccioni, “D-brane Wess-Zumino terms and U-duality,” JHEP 1011, 139 (2010) [arXiv:1009.4657 [hep-th]].", "source_...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ 0.02863920107483864, 0.026243699714541435, -0.012404725886881351, 0.0014609501231461763, -0.013838974758982658, -0.036161378026008606, 0.03823646157979965, 0.024565324187278748, 0.031675536185503006, 0.0010070257121697068, -0.06902703642845154, 0.010901816189289093, -0.014235681854188442, ...
17ca05e24d5b8cb3d03621319a9c5ca990b500fb
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Web of mixed-symmetry potentials
E^{(4)}=F, E^{(5)}=G, E^{(6)}=H, and so on) and denote the corresponding brane the E^{(n)}-brane. [Table: Exotic branes with the tension proportional to g_s^{\alpha } (\alpha \le -3) and the corresponding mixed-symmetry potentials in type II string theories.Here, n and m are non-negative integers while p (q) runs over ...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ 0.012700970284640789, 0.010206545703113079, -0.012159368023276329, -0.0015304097905755043, -0.012617059983313084, -0.015004689805209637, 0.02354065701365471, -0.0053283050656318665, 0.026500403881072998, 0.022289631888270378, -0.05351952463388443, 0.03911746293306351, -0.03231310099363327, ...
1c36e0651efffb3257b15929140a2ca8bb490511
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Exotic-brane solutions in DFT
In this section, we explain how to construct the supergravity solutions for the variety of exotic branes discussed in the previous section. If we consider only the standard branes or the defect branes, we can (at least locally) write down the solutions satisfying the standard supergravity equations of motion. However, ...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.017672929912805557, 0.016787756234407425, -0.0004468786355573684, -0.005146973766386509, -0.028142385184764862, -0.00425035459920764, 0.050760071724653244, -0.022083530202507973, 0.04624263942241669, 0.013514144346117973, -0.021625682711601257, 0.05897081270813942, -0.019717983901500702, ...
def29b089ca060a30fd8db3a974a85ea4cb1aed5
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D7-brane solution
Let us begin with the standard D7(1234567)-brane solution,{\mathrm {d}}s^2 = \tau _2^{-1/2} \,\bigl ({\mathrm {d}}x^2_{01\cdots 7} + \tau _2 \,{\mathrm {d}}x_{89}^2\bigr )\,,\qquad \operatorname{e}^{-2\Phi }= \tau _2^{2} \,, \qquad \vert {A} \rangle = \bigl (\tau _1 - \tau _2^{-1}\,\gamma ^{0 \cdots 7}\bigr )\vert {0} ...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.02576484903693199, 0.028022514656186104, -0.06449602544307709, -0.03719047084450722, 0.005853914190083742, 0.0060026454739272594, 0.005392465274780989, 0.016764694824814796, 0.053360238671302795, 0.033193789422512054, -0.016551131382584572, 0.005133138969540596, -0.020776627585291862, 0...
da823a7c2f47970a248c26115b59aaec494229de
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A quick review of DFT
In order to perform a formal T-duality, we utilize the DFT on a 20-dimensional doubled spacetime with the generalized coordinates (x^M)=(x^m,\,\tilde{x}_m) .For our purpose, it is not necessary to double the time direction, but just for notational simplicity, we double all of the directions. In DFT, all of the bosonic ...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ -0.05913553759455681, 0.006343034096062183, -0.044977184385061264, 0.009680469520390034, -0.024624550715088844, -0.00010733430099207908, -0.0013464167714118958, -0.009825409390032291, 0.05446694418787956, 0.008253954350948334, -0.023495543748140335, 0.009749124757945538, 0.01904054544866085,...
668181e646a9b7851502c23d55bd7d732064a202
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A quick review of DFT
The generalized metric and the dilaton can be parameterized asIn our convention, the sign of the B-field is opposite to the conventional DFT.(\mathcal {H}_{MN}) = \begin{pmatrix} (g-B\,g^{-1}\,B)_{mn} & -B_{mp}\,g^{pn} \\ g^{np}\,B_{pn} & g^{mn} \end{pmatrix} , \qquad \operatorname{e}^{-2d} = \sqrt{-g}\,\operatorname{e...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ -0.040520258247852325, 0.004683629143983126, -0.04445633664727211, -0.00942828319966793, 0.006678367033600807, -0.062092412263154984, -0.010702168568968773, 0.03695032373070717, 0.038018252700567245, 0.04518863186240196, -0.054616913199424744, 0.04671424254775047, 0.008383238688111305, 0.0...
7112f040416cb7079063ed27f487bb66706859b3
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A quick review of DFT
The field strength is defined as\vert {F} \rangle \equiv \partial\partial /  A       ( \partial / M M) .Unlike the standard supergravity fields, the DFT fields can depend on the generalized coordinates x^M but the consistency condition, namely the SC,\eta ^{MN}\,\partial _M \otimes \partial _N =0 \,,requires that the D...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ -0.03504271060228348, 0.008188334293663502, -0.04758848994970322, -0.05402926728129387, 0.0010054175509139895, -0.06947492063045502, 0.02646518498659134, 0.021230144426226616, 0.04517701640725136, -0.010737172327935696, -0.04438336566090584, 0.014148342423141003, -0.018879719078540802, 0.0...
2f8634a6c15bbe6c4e821fd33659efa4331bdb4f
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D8-brane solution
By using the above setup, let us construct the D8-brane solution in DFT. We start from the smeared D7 solution (REF ), and perform the formal T-duality (REF ) along the x^8-direction. We then obtain{\mathrm {d}}s^2 = \tau _2^{-1/2} \,\bigl ({\mathrm {d}}x^2_{01\cdots 8} + \tau _2 \,{\mathrm {d}}x_{9}^2\bigr )\,,\qquad ...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep11(2011)086", "end": 760, "openalex_id": "https://openalex.org/W3102933227", "raw": "O. Hohm and S. K. Kwak, “Massive type II in double field theory,” JHEP 1111, 086 (2011) [arXiv:1108.4937 [hep-th]].", "source_ref_id": "2...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.019367452710866928, 0.035957224667072296, -0.05244016274809837, -0.03403421491384506, -0.027364730834960938, -0.031805966049432755, 0.03907066956162453, 0.04914357513189316, 0.07374589145183563, 0.019397977739572525, -0.03159229829907417, 0.002808204386383295, -0.000159058443387039, 0.0...
0c66aa45960ca4235439f850a9a7d634998d3f2a
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Non-geometric fluxes and mixed-symmetry potentials
In the dual parameterization, we can define the so-called non-geometric Q-flux , , , asQ_1^{pq}\equiv Q_m{}^{pq}\,{\mathrm {d}}x^m \equiv {\mathrm {d}}\beta ^{pq} \,.The non-geometricity of the 5^2_2-brane (or the Q-brane) background was pointed out in , and as shown in , , the 5^2_2(12345,67) background has a constant...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 167, "openalex_id": "", "raw": "F. Marchesano and W. Schulgin, “Non-geometric fluxes as supergravity backgrounds,” Phys. Rev. D 76, 041901 (2007) [arXiv:0704.3272 [hep-th]].", "source_ref_id": "7c2f101314da499d3b97dacbc33620...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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en
Physics
[ -0.04980156570672989, 0.05553850904107094, -0.02432098425924778, -0.023283451795578003, -0.024198921397328377, -0.005473747383803129, 0.007476337719708681, 0.0116188395768404, 0.029142459854483604, 0.042325228452682495, -0.00712922215461731, 0.010886463336646557, -0.003658065339550376, 0.0...
99cb05324fa71a68e4b685dbf9c7082d86767518
subsection
58
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Non-geometric fluxes and mixed-symmetry potentials
The equation of motion for the \beta -field takes the form\partial _m \bigl (\operatorname{e}^{-2\tilde{\phi }}\sqrt{-\tilde{g}}\,\tilde{g}^{mn}\,\tilde{g}_{pq,\,rs}\, Q_n{}^{rs} \bigr ) = 0 \,,and this suggests to introduce the dual field strength as Q_{9,2} \equiv \operatorname{e}^{-2\tilde{\phi }} \tilde{g}_{pq,\,rs...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep03(2015)135", "end": 397, "openalex_id": "https://openalex.org/W2035516467", "raw": "Y. Sakatani, “Exotic branes and non-geometric fluxes,” JHEP 1503, 135 (2015) [arXiv:1412.8769 [hep-th]].", "source_ref_id": "ae050b5b2c3a...
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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5830ca01126b51dfbee0f6c2e3666fad86931863
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Non-geometric fluxes and mixed-symmetry potentials
In , the effective Lagrangian for the R-flux was derived from the DFT Lagrangian as (see also , , , , )\mathcal {L}\sim \sqrt{-\tilde{g}}\operatorname{e}^{-2\tilde{\phi }}\Bigl (\tilde{R} + 4\,\vert {{\mathrm {d}}\tilde{\phi }} \vert ^2 - \frac{1}{2}\,\vert {R} \vert ^2 \Bigr ) \,,where \vert {R} \vert ^2\equiv \frac{1...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 392, "openalex_id": "", "raw": "D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, “A geometric action for non-geometric fluxes,” Phys. Rev. Lett. 108, 261602 (2012) [arXiv:1202.3060 [hep-th]].", "source_ref_id": "3ce...
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ 0.003947400487959385, 0.050252124667167664, -0.029504435136914253, -0.029016252607107162, -0.012868143618106842, -0.041190266609191895, 0.028375515714287758, 0.033287838101387024, 0.011190022341907024, 0.0164913609623909, -0.048268888145685196, 0.027643244713544846, -0.010450122877955437, ...
ef1f5102098582893ddcf2dcd4f8a2c6c132788f
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Non-geometric fluxes and mixed-symmetry potentials
As it has been discussed there, D_{9,3} is the T-dual of D_{8,2} ,D_{a_1\cdots a_8,\,b_1b_2} \ \overset{T_z}{\longleftrightarrow } \ D_{a_1\cdots a_8y,\,b_1b_2y}\qquad \bigl (y\notin \lbrace a_1,\cdots ,a_8\rbrace \,,\quad \lbrace b_1,b_2\rbrace \in \lbrace a_1,\cdots ,a_8\rbrace \bigr )\,.By observing the explicit for...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1088/0264-9381/24/21/s03", "end": 973, "openalex_id": "https://openalex.org/W3101937316", "raw": "B. Wecht, “Lectures on nongeometric flux compactifications,” Class. Quant. Grav. 24, S773 (2007) [arXiv:0708.3984 [hep-th]].", "sourc...
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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06fb63d1e7d668f312b8dbdd38dcbebff56cac71
subsection
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Non-geometric fluxes and mixed-symmetry potentials
In such cases, we provide heuristic definitions of the R-fluxes by considering the symmetry of exotic branes and providing an appropriate antisymmetrization, like R^{mnp}=3\,\tilde{\partial }^{[m}\beta ^{np]} .We can again consider a definition of a non-geometric flux , Q_1^{n_1\cdots n_6}\equiv Q_m{}^{n_1\cdots n_6}\,...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep03(2015)135", "end": 383, "openalex_id": "https://openalex.org/W2035516467", "raw": "Y. Sakatani, “Exotic branes and non-geometric fluxes,” JHEP 1503, 135 (2015) [arXiv:1412.8769 [hep-th]].", "source_ref_id": "ae050b5b2c3a...
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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3d1ae1346754ea4f21ecce65a685ecfbe19b4a28
subsection
62
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Non-geometric fluxes and mixed-symmetry potentials
The mixed-symmetry potential may be defined through Q_{9,6}\equiv {\mathrm {d}}E^{(4)}_{8,6} , and in the 1_4^6(1,234567) background, we obtainE^{(4)}_{\bar{0}\cdots \bar{7},\,\bar{2}\cdots \bar{7}} = -m\,\tau _2^{-1} \,.Similarly, in the 1_4^{(1,0,6)}(1,234567,,8) background, a new locally non-geometric flux may be de...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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18c4e9a2dd889e5355167c3b7871cd2fc6b2a33e
subsection
63
130
All exotic-brane solutions in EFT
In this section, we give a prescription to construct all of the elementary exotic-brane solutions in EFT. After introducing duality transformations in Sections REF and REF , in Sections REF to REF we construct all the domain-wall solutions contained in (REF ), (REF ), and (REF ) as well as their associated R-fluxes and...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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c10e7425cb61f136bdad390fadd62d1a8512133b
subsection
64
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Duality rotations in EFT
Type II string theory compactified on an (n-1)-torus has the E_{n(n)} U-duality symmetry, which contains the \mathrm {O}(n-1,n-1) T-duality symmetry as a subgroup. The E_{n(n)} EFT is a generalization of DFT that manifests the U-duality symmetry in supergravity , , , , , , , , , , , , , , . Similar to DFT, it is define...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1088/1126-6708/2000/08/007", "end": 291, "openalex_id": "https://openalex.org/W3102742262", "raw": "P. C. West, “Hidden superconformal symmetry in M-theory,” JHEP 0008, 007 (2000) [hep-th/0005270].", "source_ref_id": "213d910a15b48...
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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46d6dac1c47e74bfe5505eaca0a2c8c525948d73
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65
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Duality rotations in EFT
In the type IIB parameterization, all of the coordinates are associated with the type IIB branes, such as P, F1/D1, D3, NS5/D5 etc., and the index \alpha represents the \mathrm {SL}(2) S-duality doublet. The winding-coordinates \mathsf {y}^{\alpha \beta }_{m_1\cdots m_7}=\mathsf {y}^{(\alpha \beta )}_{m_1\cdots m_7} co...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1093/ptep/ptx038", "end": 1268, "openalex_id": "https://openalex.org/W2585855635", "raw": "Y. Sakatani and S. Uehara, “Connecting M-theory and type IIB parameterizations in exceptional field theory,” PTEP 2017, no. 4, 043B05 (2017) [arXi...
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.05811164528131485, 0.00032595283119007945, -0.05747070908546448, 0.0005245766369625926, -0.0010129098081961274, -0.025439104065299034, 0.00616139080375433, 0.002748781582340598, 0.048406023532152176, 0.003544230479747057, -0.046391647309064865, 0.02189868874847889, 0.031802695244550705, ...
d289d16c142c5bc2afd468ad4378a6607adcdc2a
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Dual parameterization in the whole bosonic sector
In the case of DFT, the conventional fields and the dual fields are related through the expression (REF ). Here, we briefly explain how to generalize the relation (REF ) to EFT.As we already explained, the generalized metric \mathcal {M}_{IJ} in EFT can be parameterized by the bosonic fields in type IIB supergravity, w...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep03(2015)144", "end": 571, "openalex_id": "https://openalex.org/W1981362005", "raw": "C. D. A. Blair and E. Malek, “Geometry and fluxes of SL(5) exceptional field theory,” JHEP 1503, 144 (2015) [arXiv:1412.0635 [hep-th]].", ...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.06871076673269272, 0.01729973591864109, -0.012662064284086227, -0.015636887401342392, -0.007818443700671196, -0.016887838020920753, 0.008314247243106365, 0.0032513283658772707, 0.043417152017354965, 0.02977873384952545, -0.05458417534828186, 0.0252631064504385, 0.012501881457865238, 0.0...
d4e515591b9f87ece5be941d36ca4571303c3f64
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Reorganization of the generalized coordinates
In order to simplify the T-duality rule, we here consider the following redefinitions of the generalized coordinates in type II theory. The winding coordinates for P and F1 (that appear also in DFT) are defined as\big (x^m,\,\tilde{x}_m\bigr ) \equiv {\left\lbrace \begin{array}{ll} \bigl (x^m,\, y_{m\text{\tiny M}}\big...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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44a4db16c4d57ed14d91d2c09f69ea1a4d8cc9ec
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Reorganization of the generalized coordinates
The winding coordinates for the D-branes y^{\text{\tiny D}}_{m_1\cdots m_p} (p=0,\cdots ,7) and the solitonic branes 5_2^n (n=0,1,2) are denoted as&(y^{\text{\tiny D}}_{m_1\cdots m_p}) \equiv \bigl (\underbrace{-x^\text{\tiny M}}_{\text{D0}},\,\underbrace{-\mathsf {y}^2_m}_{\text{D1}},\,\underbrace{y_{m_1m_2}}_{\text{D...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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67521efee13d5348e7b42aa348c9cde5cbcc8ca9
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Reorganization of the generalized coordinates
\end{array}\right.}The winding coordinates for the exotic p_3^{7-p}-branes (p=0,\cdots ,7) and the (1^6_4,\,0^{(1,6)}_4)-branes are called\begin{split} &(y^{\text{\tiny E}}_{m_1\cdots m_7,\,n_1\cdots n_{7-p}}) \equiv \bigl (\underbrace{y_{m_1\cdots m_7\text{\tiny M},\,n_1\cdots n_7\text{\tiny M},\,\text{\tiny M}}}_{0^7...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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1014a9e7e5ee455b1e502888e7de22e0767cecd5
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Reorganization of the generalized coordinates
\end{array}\right.}The remaining eight coordinates in the E_{8(8)} exceptional space,&y_{m_1\cdots m_6\text{\tiny M},\,n}\quad \bigl (n\notin \lbrace m_1\cdots m_6\rbrace \bigr )\,,\quad y_{m_1\cdots m_7\text{\tiny M}}\qquad (\text{IIA})\,, \\ &\mathsf {y}_{m_1\cdots m_6,\,n}\quad \bigl (n\notin \lbrace m_1\cdots m_6\r...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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03e4d2ad232bd3dcf767131c6e810921502053c8
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First two examples of domain-wall solutions in EFT
Before considering all of the “elementary” domain-wall solutions, let us begin with two simple examples.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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3d87e17d49621cd15e4e558c2c58e02766c4a6fc
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Dual parameterization for the
For the 7_3 background, the non-vanishing fields are the (g_{\mu \nu },\,g_{mn},\,\Phi ,\,C_0) . In this case, (REF ) and (REF ) are reduced to\begin{split} &g^{\text{\tiny E}}_{mn} = \tilde{g}^{\text{\tiny E}}_{mn}\,,\qquad \bigl (m_{\alpha \beta }\bigr ) = \operatorname{e}^{\Phi }\,\begin{pmatrix} \operatorname{e}^{-...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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a63f890b7c1776c7f930bcf70818ba4770cae4b2
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Dual parameterization for other
We can similarly obtain the dual parameterizations for other p-brane solutions in (REF ) and (REF ). However, in general, a direct comparison of the generalized metrics is very complicated.For simplicity, we instead use the T-duality rules (REF ) and (REF ). Then, we can easily obtain the dual parameterization of the p...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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f04daab466f19454436c616e646b04d64a341380
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Non-geometric flux and mixed-symmetry potentials
As discussed in , backgrounds of the exotic p_3^{7-p}-branes are the magnetic sources of the non-geometric P-fluxes. The non-geometric P-fluxes were introduced in , , and in particular, a P-flux P_m{}^{pq} is S-dual of the Q-flux. They are roughly defined as (see for more details)P_1^{n_1\cdots n_{7-p}} \equiv P_m{}^{n...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep03(2015)135", "end": 116, "openalex_id": "https://openalex.org/W2035516467", "raw": "Y. Sakatani, “Exotic branes and non-geometric fluxes,” JHEP 1503, 135 (2015) [arXiv:1412.8769 [hep-th]].", "source_ref_id": "ae050b5b2c3a...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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79b8de35378668974ac13faf1c77a82c1f39368a
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Non-geometric flux and mixed-symmetry potentials
In the p_3^{7-p}(1\cdots p,p+1\cdots 7) solution, we obtainE_{\bar{0}\bar{1}\bar{2}\bar{3}\bar{4}\bar{5}\bar{6}\bar{7},\,\overline{p+1}\cdots \bar{7}} = -m\,\tau _2^{-1} \,.Similarly, in the p_3^{(1,7-p)}(1\cdots p,p+1\cdots 7,8) background, the derivative of the \gamma -field gives a locally non-geometric flux introdu...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep11(2015)020", "end": 414, "openalex_id": "https://openalex.org/W2252466802", "raw": "E. A. Bergshoeff, V. A. Penas, F. Riccioni and S. Risoli, “Non-geometric fluxes and mixed-symmetry potentials,” JHEP 1511, 020 (2015) [arXiv:15...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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f25a463e223d1b5b875efa29ab3af4b6df6e573e
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Non-geometric flux and mixed-symmetry potentials
If we also introduce the potential as R_{10,8-p,1} \equiv {\mathrm {d}}E_{9,8-p,1} , we obtainE_{\bar{0}\bar{1}\bar{2}\bar{3}\bar{4}\bar{5}\bar{6}\bar{7}\bar{8},\,\overline{p}\cdots \bar{8},\bar{8}} = -m\,\tau _2^{-1} \,,in the p_3^{(1,7-p)}(1\cdots p,p+1\cdots 7,8) background, suggesting the T-duality ruleE_{a_1\cdots...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep12(2016)114", "end": 601, "openalex_id": "https://openalex.org/W2542887935", "raw": "D. M. Lombardo, F. Riccioni and S. Risoli, “P fluxes and exotic branes,” JHEP 1612, 114 (2016) [arXiv:1610.07975 [hep-th]].", "source_ref...
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ 0.002555701183155179, 0.03314019739627838, -0.03692416101694107, 0.001345557626336813, -0.01187065988779068, 0.0036199409514665604, 0.01361006312072277, 0.06603626906871796, 0.005973475053906441, 0.00808669626712799, -0.025221338495612144, 0.02496195398271084, -0.015189257450401783, -0.036...
07bf12a4234d3060caa6bf38a3ed2f4a167e0c0b
subsection
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A short summary
Up to here, we have discussed the defect-brane solutions\text{D7}\ (\ref {eq:D7-soln}),\quad 5^2_2\ (\ref {eq:522-soln}),\quad p_3^{7-p}\ (\ref {eq:p(7-p)3-soln}),\quad 1_4^{(1,0,6)}\ (\ref {eq:164-soln})\,,and the domain-wall-brane solutions\text{D8}\ (\ref {eq:D8-soln}),\quad 5^3_2\ (\ref {eq:532-soln}),\quad p_3^{(1...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.007334060966968536, 0.03228054940700531, -0.027749676257371902, -0.04399674013257027, -0.011571264825761318, -0.026483474299311638, 0.02471384033560753, -0.014393524266779423, 0.04643761366605759, 0.027124203741550446, -0.019786328077316284, 0.0076811229810118675, -0.019054066389799118, ...
65a077cdd209ce376e709f75988894ebd5b50c87
subsection
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A short summary
Further, the set of indices \lbrace A\rbrace in the R-fluxes can be found from the set of indices \lbrace A\rbrace in the mixed-symmetry potentials, which are consistent with the general rule (REF ). In fact, this appears to be a general structure as we see below.In the following, we will firstly introduce a generaliza...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.022585539147257805, 0.0028441757895052433, -0.005081746727228165, 0.025011960417032242, -0.011903190053999424, -0.020647456869482994, 0.0015642012003809214, 0.014573777094483376, 0.019335053861141205, 0.00818725861608982, -0.010201644152402878, 0.0291933361440897, -0.013185071758925915, ...
a2037dba8308172aeb7b24e16e7bf29c750f368c
subsection
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Locally non-geometric fluxes
As we have already discussed, a domain-wall brane, say the b^{(c_s,\cdots ,c_2)}_n-brane, is the magnetic source of the non-geometric flux with a set of antisymmetrized indices, R^{c_2+\cdots +c_s,\cdots ,c_{s-1}+c_{s},c_s}, which is a U-duality version of the familiar R-flux (see , , for definitions of locally non-geo...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep03(2015)144", "end": 382, "openalex_id": "https://openalex.org/W1981362005", "raw": "C. D. A. Blair and E. Malek, “Geometry and fluxes of SL(5) exceptional field theory,” JHEP 1503, 144 (2015) [arXiv:1412.0635 [hep-th]].", ...
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.03128856420516968, 0.05332792177796364, -0.01695687510073185, 0.004067513160407543, -0.01686529815196991, -0.0038481117226183414, -0.023336689919233322, 0.010813632979989052, 0.06373709440231323, 0.021245697513222694, -0.027198156341910362, 0.023977722972631454, -0.02721341885626316, 0....
2ec160a1d8d64ddfff52d804edc9f333cb214f50
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Locally non-geometric fluxes in type IIA theory/
The obtained R-fluxes in type IIA theory and the corresponding domain-wall branes can be summarized as follows:\begin{split} &\underline{R_{(2)}^{3}\ \leftrightarrow \ \text{$5^3_2$-brane:}} \\ &R_{(2)}^{m_1m_2m_3} \equiv 3\,\tilde{\partial }^{[m_1} \beta ^{m_2m_3]} \,, \end{split} \\ \begin{split} &\underline{R_{(3)}^...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.0351485013961792, 0.08183010667562485, -0.029397206380963326, -0.033470407128334045, -0.02231868915259838, -0.014668092131614685, 0.00739125395193696, 0.0560789480805397, 0.03459930792450905, 0.01691826805472374, -0.02547656185925007, 0.015369841828942299, -0.032036393880844116, 0.01054...
f21b32779d6b9d8e5f28952c30308cdb57bdccb5
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Locally non-geometric fluxes in type IIA theory/
\end{split}Here, the vector field A^m_n\equiv \tilde{g}^{mn}/\tilde{g}^{nn} is the graviphoton, which is T-dual of the \beta -field; A^m_y\ \overset{T_y}{\leftrightarrow }\ \beta ^{my} . We have attached the subscript (n) to the R-flux that is associated with the exotic brane b^{(c_s,\cdots ,c_2)}_{n} .In the type IIA ...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep03(2015)144", "end": 1365, "openalex_id": "https://openalex.org/W1981362005", "raw": "C. D. A. Blair and E. Malek, “Geometry and fluxes of SL(5) exceptional field theory,” JHEP 1503, 144 (2015) [arXiv:1412.0635 [hep-th]].", ...
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.05637423321604729, 0.010194365866482258, -0.006489751394838095, -0.0034756988752633333, -0.009202399291098118, -0.03104092925786972, -0.001517518307082355, 0.024341337382793427, 0.04166260361671448, 0.018938934430480003, -0.055763792246580124, 0.009805209934711456, -0.019549375399947166, ...
1f6ae555561be4ee41ae8b3b987a3d583619d563
subsection
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Locally non-geometric fluxes in type IIB theory/
In type IIB theory, the R-fluxes and the corresponding domain-wall branes are as follows:\begin{split} &\underline{R_{(2)}^{3}\ \leftrightarrow \ \text{$5^3_2$-brane:}} \\ &R_{(2)}^{m_1m_2m_3} \equiv 3\,\tilde{\partial }^{[m_1} \beta ^{m_2m_3]} \,, \end{split} \\ \begin{split} &\underline{R_{(3)}^{6,1}\ \leftrightarrow...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.03198804333806038, 0.050362855195999146, -0.024494662880897522, -0.009843649342656136, -0.0096528809517622, -0.0021175292786210775, 0.010904321447014809, 0.0427015982568264, 0.024464139714837074, 0.019092101603746414, -0.02866104431450367, 0.0010921490611508489, -0.035070862621068954, 0...
6bcaf73861b85c760ba4029e8d761f5f3e712a05
subsection
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Locally non-geometric fluxes in type IIB theory/
\end{split}For an exotic brane that is self-dual under the S-duality, we can check that the associated R-flux also behaves as a singlet. Under the S-duality, the scalar \gamma is mapped to the R–R 0-form -C_0 , but since C_0 is non-linear in terms of the dual fields, we have just truncated C_0 in the above expressions.
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.0802021399140358, 0.06573645770549774, -0.03108290769159794, 0.0027943335007876158, -0.052369434386491776, -0.022415705025196075, 0.02598634734749794, 0.03698820248246193, 0.00602355320006609, 0.04278668388724327, -0.01911972649395466, 0.025345463305711746, -0.013237320818006992, 0.0131...
2f4ad66dd5780db886a77e9d06279ecb32bb0ed1
subsection
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Locally non-geometric fluxes in M-theory/
We can easily uplift the R-fluxes obtained in type IIA theory to M-theory.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ 0.0013107004342600703, 0.03888983651995659, -0.010088768787682056, 0.022146450355648994, -0.01640760339796543, -0.004678075201809406, -0.005143593065440655, 0.052534859627485275, 0.00441860593855381, 0.008081698790192604, -0.036295145750045776, -0.026755841448903084, 0.01028718613088131, 0...
137535004f3d526dfbe76aabe336b7dc1c85c1f8
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Locally non-geometric fluxes in M-theory/
The results are as follows:\begin{split} &\underline{R^{1,1}\ \leftrightarrow \ \text{$8^{(1,0)}_{12}$-brane:}} \\ &R^{i,\,j} \equiv \partial ^{ki}A^{j}_k \,, \end{split} \\ \begin{split} &\underline{R^{4,1}\ \leftrightarrow \ \text{$5^{(1,3)}_{15}$-brane:}} \\ &R^{i_1\cdots i_4,\,j} \equiv \frac{4!}{2!\,2!}\,\partial ...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.000632388168014586, 0.06989654153585434, -0.05506260320544243, -0.045844804495573044, -0.023899123072624207, -0.013880109414458275, 0.00663483003154397, 0.03250646963715553, -0.0009724280098453164, 0.0009166290401481092, -0.030186759307980537, 0.0019009798998013139, -0.0705680325627327, ...
ef722dc7bc90afd3aa20e0b940fa908e1f484584
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Locally non-geometric fluxes in M-theory/
\end{split}Note that the A_{\text{\tiny M}}^m is equal to the -\gamma ^m in type IIA theory while A^{\text{\tiny M}}_m is a complicated non-linear expression that will be related to R–R 1-form C_m.By using the identities such as (REF ), the fluxes R^{4,1}, R^{7,4}, and R^{7,7} appear to be consistent with the locally n...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep01(2018)050", "end": 388, "openalex_id": "https://openalex.org/W2766746536", "raw": "D. Lüst, E. Malek and M. Syvari, “Locally non-geometric fluxes and missing momenta in M-theory,” JHEP 1801, 050 (2018) [arXiv:1710.05919 [hep-t...
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.03059021383523941, 0.04552678391337395, -0.01745396852493286, -0.027630362659692764, -0.04583192244172096, -0.0063697826117277145, -0.020184963941574097, 0.03098689578473568, 0.023404184728860855, -0.0048021296970546246, -0.03548770025372505, -0.0015676531475037336, 0.012396284379065037, ...
4afa8585c042ed92172882cf1935d7a29e0e949d
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Mixed-symmetry potentials in EFT
In the previous subsection, we have introduced various R-fluxes on a heuristic basis. Similar to the R-fluxes in DFT, we here consider the introduction of the dual field strength to the R-flux in type II theory, R_{(n)}^{m_1\cdots m_{a_1},\,\cdots ,\,p_1\cdots p_{a_s}} . As we check in the next subsection, if we define...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.035650331526994705, 0.026707224547863007, 0.005162124987691641, 0.013956433162093163, -0.013391765765845776, -0.004826377145946026, 0.010888917371630669, 0.056924544274806976, 0.0431588739156723, 0.029271118342876434, -0.051735710352659225, 0.02128947339951992, -0.03198762610554695, 0.0...
d2a9585611f28d2e48a795a64907fbacc2aecac7
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Mixed-symmetry potentials in EFT
The transformation rule (at the linearized level) is perfectly consistent with the rule , ,E^{(n)}_{\underbrace{{\tiny \cdots y,\cdots y,\cdots y}}_{p}}\quad \overset{T_y}{\leftrightarrow }\quad E^{(n)}_{\underbrace{\scriptsize \cdots y,\cdots y,\cdots y}_{n-p}} \,.We thus expect that the dual potentials E^{(n)}_{9,a_1...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep12(2016)114", "end": 266, "openalex_id": "https://openalex.org/W2542887935", "raw": "D. M. Lombardo, F. Riccioni and S. Risoli, “P fluxes and exotic branes,” JHEP 1612, 114 (2016) [arXiv:1610.07975 [hep-th]].", "source_ref...
10.1007/JHEP09(2018)072
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.027117233723402023, 0.03470151126384735, -0.002823122078552842, -0.016801392659544945, -0.008141273632645607, -0.005321966949850321, 0.003933296073228121, 0.03378590568900108, 0.034854114055633545, 0.033511221408843994, -0.0333891436457634, 0.034304749220609665, -0.017625438049435616, -...
ce5d47246678b75411ede2a2251ae9310ff7dd49
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Exotic-brane solutions in type II theory
Utilizing the technique of the duality rotations in EFT, we here provide a full list of the type II domain-wall solutions in EFT. The structure of the solutions is quite similar to the domain-wall solutions discussed above, and only a certain gauge field contains a winding-coordinate dependence. Similar to the domain-w...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.05201415717601776, 0.002974254311993718, -0.012141214683651924, 0.006700180470943451, -0.02138257957994938, 0.013980330899357796, 0.03424875810742378, 0.05723388493061066, 0.021733613684773445, 0.027212806046009064, -0.002054696436971426, 0.019459521397948265, -0.002352312672883272, 0.0...
a624892079b5ff9c1d4b65e3d8d291ef76e10b9b
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E
By considering S-dual of the 5^3_2-brane or the 4^{(1,3)}_3-brane, we obtain the backgrounds of a T-duality family, E^{(4;3)}-branes.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.0098090386018157, 0.03578849509358406, -0.04433136060833931, 0.00683429092168808, -0.012425290420651436, -0.020777465775609016, 0.03334767743945122, 0.014515240676701069, -0.007757225539535284, 0.023157263174653053, -0.012669372372329235, 0.002492304192855954, -0.026604918763041496, 0.0...
7f66b62f4f8f4cdd2534f18011d0f12cf8b7ea7c
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The explicit forms of the dual fields and the locally non-geometric fluxes are as follows:\begin{split} &\underline{{5^3_4(12345,678):} \qquad \bigl \lbrace \,R_{(4)}^{3},\,E^{(4)}_{9,3}\,\bigr \rbrace } \\ &{\mathrm {d}}\tilde{s}^2 = \tau _2\, {\mathrm {d}}x^2_{01\cdots 5} + {\mathrm {d}}x^2_{678} + \tau _2^2 \,{\math...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.04005544260144234, 0.0425570011138916, -0.043472204357385635, -0.03212366998195648, -0.02408512681722641, -0.007748729549348354, 0.031940631568431854, 0.03676070645451546, 0.012012056075036526, 0.024786783382296562, -0.03514384478330612, 0.007531368639320135, -0.0267544724047184, -0.010...
e870a031ad462f21827b62f0917b205a7f1c624a
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\end{split}Similarly, by performing the S-duality in the 2^{(1,5)}_3 or the 2^{(3,3)}_4 solution, we obtain a T-duality chain of the E^{(5;6)}-branes.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ 0.02638738416135311, 0.03671951964497566, -0.04019917547702789, 0.009401173330843449, -0.03314829245209694, -0.010110840201377869, 0.021167902275919914, 0.007424790412187576, 0.0006653123418800533, 0.011629373766481876, -0.023228224366903305, -0.00273374211974442, -0.021579965949058533, 0....
d7bcb72316bf7b560f65523a659fe87b31c238b9
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The dual fields and the locally non-geometric fluxes are as follows:\begin{split} &\underline{{2^{6}_5(12,345678):} \qquad \bigl \lbrace \,R_{(5)}^{6},\,E^{(5)}_{9,6}\,\bigr \rbrace } \\ &{\mathrm {d}}\tilde{s}^2 = \tau _2^{3/2}\, \bigl ({\mathrm {d}}x^2_{012} + \tau _2\,{\mathrm {d}}x_{9}^2\bigr ) + \tau _2^{1/2}\,{\m...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.05619600787758827, 0.029409853741526604, -0.04890456050634384, -0.029409853741526604, -0.02436075545847416, 0.003939364571124315, 0.0068948413245379925, 0.02429973892867565, 0.02146248146891594, 0.025718368589878082, -0.039996180683374405, 0.0007598435622639954, -0.035755548626184464, -...
2c693efe24e2cd2ce421e7f091e03356a67ba228
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\end{split}We can repeat the duality transformations and obtain the following solutions,\begin{split} &\underline{{1^{(4,3)}_6(1,678,2345):} \qquad \bigl \lbrace \,R_{(6)}^{7,4},\,E^{(6)}_{9,7,4}\,\bigr \rbrace } \\ &{\mathrm {d}}\tilde{s}^2 = \tau _2^2\, {\mathrm {d}}x^2_{01} + {\mathrm {d}}x_{2345}^2 + \tau _2\,{\mat...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ -0.03647204115986824, 0.04776464030146599, -0.03143615275621414, -0.03641100227832794, -0.03949357569217682, 0.03549538552761078, 0.050572533160448074, 0.053563542664051056, -0.0007611059118062258, 0.010087037459015846, -0.035129137337207794, 0.02549991011619568, -0.0015622699866071343, -0...
1b00f956703bc639fc1f71698db1a046830551f3
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\end{split}Note that the 1^{(2,4,1)}_6-brane is self-dual under the S-duality transformation. Apparently, the above 1^{(2,4,1)}_6 is not invariant under the S-duality transformation, but since the R-flux is invariant under the S-duality, the apparent non-invariance is due to a particular gauge choice.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ -0.007760948967188597, 0.09609229862689972, -0.023137852549552917, -0.0018295844784006476, -0.054792147129774094, -0.018269136548042297, 0.0017046233406290412, 0.03821713849902153, 0.012248105369508266, 0.008501176722347736, -0.0021958830766379833, -0.01465193834155798, -0.01804019883275032,...
f51c3e94432d78bb40f45032d61d95f726372820
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The R-flux, or the magnetic charge of the 1^{(2,4,1)}_6-brane is invariant under the S-duality.We can further obtain the following family of solutions:\begin{split} &\underline{{1^{(7,0)}_7(1,,2345678):} \qquad \bigl \lbrace \,R_{(7)}^{7,7},\,E^{(7)}_{9,7,7}\,\bigr \rbrace } \\ &{\mathrm {d}}\tilde{s}^2 = \tau _2^{5/2}...
{ "cite_spans": [] }
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[ "hep-th" ]
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Physics
[ -0.01024373434484005, 0.0633997917175293, -0.039846066385507584, -0.03261519595980644, -0.015476200729608536, -0.009099609218537807, 0.021418023854494095, 0.04744305834174156, 0.031104950234293938, -0.0018801791593432426, -0.000010309045137546491, -0.009183512069284916, -0.02741323970258236,...
5a4dcc768097696694ffc3173ee99861b7ea225b
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E
\end{split}Finally, by performing the S-duality in the 1^{(7,0,0)}_7 background, we obtain\begin{split} &\underline{{1^{(7,0,0)}_8(1,,,2345678):} \qquad \bigl \lbrace \,R_{(8)}^{7,7,7},\,E^{(8)}_{9,7,7,7}\,\bigr \rbrace } \\ &{\mathrm {d}}\tilde{s}^2 = \tau _2^{3}\, \bigl ({\mathrm {d}}x^2_{01} + \tau _2\,{\mathrm {d}}...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.053024325519800186, 0.0570843368768692, -0.047743260860443115, -0.02081899344921112, -0.03038901463150978, 0.029015326872467995, 0.00806659646332264, 0.057816967368125916, -0.013721609488129616, 0.0029477039352059364, -0.02744321897625923, 0.005948828998953104, -0.030862173065543175, -0...
8b899bc33f8f3cc4dc649502cb25392d5e4b6767
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Exotic-brane solutions in M-theory
By uplifting the defect-brane solutions in type II theories to M-theory, we obtain the following defect-brane solutions:\begin{split} &\underline{{5_{12}^{3}(12345,67z):} \qquad \bigl \lbrace \,S_1^{3},\,E_{9,3}\,\bigr \rbrace } \\ &{\mathrm {d}}\tilde{s}^2 = \tau _2^{1/3}\, \bigl ({\mathrm {d}}x^2_{012345} + \tau _2\,...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
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adf68beffe299581ca69ce1be1f9f1bb242d3dd3
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Exotic-brane solutions in M-theory
The direction z represents one of the internal ones that is not necessary to be the M-theory direction, which we denote M.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.03643412888050079, 0.01670660264790058, -0.045161228626966476, 0.022901015356183052, -0.04360499978065491, -0.0017765070078894496, -0.015020686201751232, -0.019483407959342003, -0.02904965542256832, 0.019529180601239204, -0.009062760509550571, -0.05642102286219597, 0.024304674938321114, ...
c9937a17cc29f984b8b1a6f2af86b4ad74e17b34
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Exotic-brane solutions in M-theory
If we define the dual field strengths,\begin{split} S_{10,\bar{m}_1\bar{m}_2\bar{m}_3} &\equiv \tilde{G}_{\bar{m}_1\bar{m}_2\bar{m}_3,\bar{n}_1\bar{n}_2\bar{n}_3}\,\tilde{*}_{11} S_{1}^{\bar{n}_1\bar{n}_2\bar{n}_3} \equiv {\mathrm {d}}E_{9,\bar{m}_1\bar{m}_2\bar{m}_3}\,, \\ S_{10,\bar{m}_1\cdots \bar{m}_6} &\equiv \til...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.030277835205197334, 0.050422362983226776, -0.030628839507699013, -0.02486017905175686, -0.007393957115709782, -0.03415413200855255, 0.027607159689068794, 0.03183445706963539, 0.04382960870862007, 0.01393329817801714, -0.036962155252695084, 0.010255396366119385, -0.026584671810269356, 0....
48563d1c16768b43ca93d0619455efe15b541cd4
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Exotic-brane solutions in M-theory
\end{split}Again, by computing the dual mixed-symmetry potentials through (REF ), we obtainE_{\bar{0}\cdots \bar{9},\cdots ,\cdots ,\cdots } = -m\,\tau _2^{-1}\,.
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
[ 0.033148251473903656, 0.011453850194811821, -0.017093021422624588, -0.0260668583214283, -0.012835027649998665, -0.005219476297497749, 0.008874636143445969, 0.04648691415786743, 0.009515623562037945, 0.021732555702328682, -0.031194763258099556, 0.03598691523075104, -0.02319767139852047, 0.0...
0f9caa1401a1733eeeb70d91173090e65063e3f8
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Solutions for space-filling branes
We have completed the full list of the “elementary” domain-wall solutions. We can straightforwardly continue the duality rotations to obtain all of the space-filling branes given in Figures REF –REF or their M-theory extensions. Since there are too many space-filling branes in EFT, we will just show several examples an...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
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Physics
[ -0.026183616369962692, 0.04531779885292053, -0.021514510735869408, -0.026534562930464745, -0.02323872223496437, -0.01611299440264702, 0.025191813707351685, 0.013175730593502522, 0.056395482271909714, 0.014365894719958305, -0.011062425561249256, 0.015403473749756813, -0.03991628438234329, 0...
f390a30546b0be9bdb2b3caf09e6ad0c738b1068
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Solutions for space-filling branes
By performing a T-duality along the x^9-direction in the 2^{6}_5(12,345678) solution, we obtain the 2^{(1,0,0,6)}_5(12,345678,9) solution,{\mathrm {d}}\tilde{s}^2 = \tau _2^{3/2}\, {\mathrm {d}}x^2_{012} + \tau _2^{1/2}\,{\mathrm {d}}x^2_{345678} + \tau _2^{-5/2}\,{\mathrm {d}}x_{9}^2 \,,\qquad \operatorname{e}^{-2\til...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep07(2018)001", "end": 845, "openalex_id": "https://openalex.org/W2794853498", "raw": "T. Kimura, S. Sasaki and K. Shiozawa, “Worldsheet instanton corrections to five-branes and waves in double field theory,” JHEP 1807, 001 (2018)...
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[ "hep-th" ]
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Physics
[ -0.012717949226498604, 0.05667002126574516, -0.03762742877006531, -0.018966300413012505, -0.017928723245859146, 0.00581729831174016, 0.0068396166898310184, 0.021667052060365677, 0.04675200581550598, 0.026092013344168663, -0.015075385570526123, -0.01537292543798685, -0.00978831946849823, 0....
8c6edd4bc7ed821dd1c74277e5eca24a0ba17a28
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Projection condition for Killing spinors
As it is well known, actions of the standard type II branes, such as the D-branes, are invariant under the half of the spacetime supersymmetry, which is generated by the 32-component Majorana–Weyl Killing spinors \varepsilon _1 and \varepsilon _2 satisfying\Gamma ^{11}\,\varepsilon _1 = \varepsilon _1 \,,\qquad \Gamma ...
{ "cite_spans": [] }
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[ "hep-th" ]
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Physics
[ -0.004830517340451479, 0.03296656534075737, -0.029425712302327156, 0.001742763677611947, -0.0031592957675457, -0.013339249417185783, 0.01674274168908596, 0.03589692711830139, 0.042795486748218536, 0.021825086325407028, -0.02402285858988762, 0.014048946090042591, -0.02539646439254284, -0.02...
52dcac2f794770c3a0fafc7fd965c611d8f7337a
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Projection condition for Killing spinors
Then, the projection condition for each type II brane is expressed as follows (see for a textbook):\begin{split} \text{P(1)}:&\quad \bigl ({1}\mp \gamma ^{01}\,\mbox{1}\hspace{-2.5pt}\mbox{l}\bigr )\,\epsilon =0\,, \qquad \text{F1(1)}:\quad \bigl ({1}\mp \gamma ^{01}\,\sigma _3\bigr )\, \epsilon =0 \,, \\ \text{NS5(123...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 1101, "openalex_id": "https://openalex.org/W1876733565", "raw": "T. Ortín, “Gravity and strings,” Cambridge University Press.", "source_ref_id": "3f0afc7b3ec1642831237394def0cc4da7bc038e", "start": 0 }, { ...
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Physics
[ -0.028992483392357826, 0.027161380276083946, 0.008331524208188057, -0.0027466563042253256, -0.01290928479284048, 0.01982170343399048, -0.022736210376024246, 0.01513712853193283, 0.06964299827814102, 0.02963337115943432, -0.03497409075498581, 0.023697540163993835, -0.028855150565505028, -0....
2980bcd55c37fe532278bc0edcd6f8c700d595a7
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Projection condition for Killing spinors
The projection condition for an exotic brane that electrically couples to the mixed-symmetry potential E^{(n)}_{m_1\cdots m_{a_1},\,\cdots ,\,n_1\cdots n_{a_s}} is given by\bigl ({1}\mp \gamma ^{m_1\cdots m_{a_1}}\cdots \gamma ^{n_1\cdots n_{a_s}}\,\mathcal {O}\bigr )\,\epsilon = 0\,,where \mathcal {O} is a 2\times 2 m...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.021319309249520302, 0.007668542210012674, 0.0011817566119134426, -0.028369789943099022, -0.015840690582990646, -0.029361741617321968, 0.014513001777231693, 0.008805470541119576, 0.03662587329745293, 0.049292318522930145, -0.043523743748664856, 0.03177294507622719, -0.034611448645591736, ...
e0a89e4d556dc34f9795b1afe32321d5a6467bd9
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Exotic brane solutions in deformed supergravities
In the previous sections, we have constructed various exotic-brane solutions in DFT/EFT. Unlike the case of the standard branes or the defect branes, the obtained solutions explicitly depend on the dual winding coordinates. In this section, we explain that the winding-coordinate dependence in the domain-wall solutions ...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 627, "openalex_id": "", "raw": "E. Bergshoeff, M. de Roo, M. B. Green, G. Papadopoulos and P. K. Townsend, “Duality of type II 7-branes and 8-branes,” Nucl. Phys. B 470, 113 (1996) [hep-th/9601150].", "source_ref_id": "407d1...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.02272588387131691, 0.036752134561538696, -0.03115079179406166, -0.022786933928728104, -0.029304027557373047, -0.015796702355146408, 0.02918192744255066, -0.011088216677308083, 0.04435286670923233, 0.02152014523744583, -0.03311965614557266, 0.038736261427402496, -0.015033576637506485, 0....
a98fcdaa9d99b17df8d3d5e1d04c429988553e2e
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Generalized type II supergravity
In order to get a feeling of the deformed supergravity, it is instructive to review the derivation of GSE , from DFT , (see also for a derivation from EFT).
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 159, "openalex_id": "", "raw": "G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A. A. Tseytlin, “Scale invariance of the \\eta -deformed AdS_5\\times S^5 superstring, T-duality and modified type II equations,” Nucl. Phys. B 903, ...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.02449469268321991, 0.0039336490444839, -0.014612877741456032, -0.02791326679289341, -0.014284755103290081, -0.06538022309541702, 0.06672323495149612, 0.009057695046067238, -0.003941279835999012, 0.044685643166303635, -0.024143679067492485, -0.00568109005689621, -0.033178482204675674, 0....
2aa74e39b407d09dde9439d1c2d689b7e14e6279
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Bosonic sector of type II DFT
The equations of motion of the type II DFT are given as\mathcal {R}_{MN} + \mathcal {E}_{MN} = 0 \,,\qquad \mathcal {R}= 0 \,, \qquad \partial\partial /   K  F = 0 , where \mathcal {R}_{MN} and \mathcal {R} are the generalized Ricci tensor/scalar, and \mathcal {K} contains the information of \mathcal {H}_{MN} , and t...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 417, "openalex_id": "", "raw": "O. Hohm, S. K. Kwak and B. Zwiebach, “Unification of type II strings and T-duality,” Phys. Rev. Lett. 107, 171603 (2011) [arXiv:1106.5452 [hep-th]].", "source_ref_id": "303d0b963988aa94e475328...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.040352385491132736, 0.007787369657307863, -0.04206171631813049, -0.0024705154355615377, -0.005257714539766312, -0.017200129106640816, -0.005154696758836508, 0.015155037865042686, 0.024678446352481842, 0.0251820869743824, -0.031592074781656265, 0.006993752438575029, -0.004246615804731846, ...
ee2b97282cd45aa2b475da477296fdfe0d0e94ea
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Bosonic sector of type II DFT
Regarding the R–R field, since the field strength F takes the formF=\operatorname{e}^{-\Phi }\operatorname{e}^{-B_2\wedge }\hat{\mathcal {F}} \,,from (REF ), we suppose that the R–R fields have the following winding-coordinate dependence:F(x) = \operatorname{e}^{-I^m\,\tilde{x}_m} \mathsf {F}(x^i) \,.Since I^m triviall...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
[ -0.06138884648680687, 0.017421983182430267, -0.025431213900446892, -0.0367966927587986, -0.014393731951713562, -0.024485362693667412, 0.03826123848557472, 0.02942820079624653, 0.011190039105713367, 0.020473118871450424, -0.05095396190881729, 0.006041248328983784, -0.008909315802156925, 0.0...
d0fcf3a850d4d889f90b6ada322c652834e7b99f
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Bosonic sector of type II DFT
\end{split}These are precisely the generalized type II supergravity equations of motion , . When the winding-coordinate dependence vanishes (i.e. I^m=0), they have the same form as the usual supergravity equations of motion.In this manner, we can consider a slight modification of the supergravity equations of motion by...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 629, "openalex_id": "", "raw": "G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A. A. Tseytlin, “Scale invariance of the \\eta -deformed AdS_5\\times S^5 superstring, T-duality and modified type II equations,” Nucl. Phys. B 903, ...
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
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Physics
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251841411b9be35bce275b58b102cb523b3c1aa7
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Another viewpoint in terms of the Scherk–Schwarz reduction
As discussed in the addendum of , the ansatz for the dilaton (REF ) can be understood as the Scherk–Schwarz ansatz in DFT , , , , (see also where the derivation of GSE from a Scherk–Schwarz compactification of EFT was originally discussed). An ansatz\mathcal {H}_{MN}(x,y) = (U^{\mathrm {T}})_M{}^K(y)\, \hat{\mathcal {H...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep04(2017)123", "end": 242, "openalex_id": "https://openalex.org/W2550621181", "raw": "Y. Sakatani, S. Uehara and K. Yoshida, “Generalized gravity from modified DFT,” JHEP 1704, 123 (2017) [arXiv:1611.05856 [hep-th]].", "sou...
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Physics
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8aeff5f9217bf25e9e24b3669f713bbd631a0efb
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D8 solutions in the Romans massive type IIA supergravity
Before considering further new examples, let us briefly go back to the well-studied D8-brane solution (REF ). In this case, the R–R 1-form potential A_1 includes a linear winding-coordinate dependence,A_1(x) = \hat{A}_1(x^i) + m\,\tilde{x}_8\,{\mathrm {d}}x^8 \,,where \hat{A}_1(x^i) does not include the x^8 dependence ...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep11(2011)086", "end": 542, "openalex_id": "https://openalex.org/W3102933227", "raw": "O. Hohm and S. K. Kwak, “Massive type II in double field theory,” JHEP 1111, 086 (2011) [arXiv:1108.4937 [hep-th]].", "source_ref_id": "2...
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Physics
[ -0.03525408357381821, 0.021442418918013573, -0.016818182542920113, -0.02408265881240368, -0.016207721084356308, -0.007031739689409733, 0.025257796049118042, 0.05533822625875473, 0.03345322608947754, 0.017443902790546417, -0.045601386576890945, -0.0013802126049995422, -0.0026287948712706566, ...
06c23ed2aac15c1badb2ceefed2e7af963f41d63
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KK8A and M9 solutions
Let us consider the solution of the 7_3^{(1,0)}(1\cdots 7,,8)-brane (), which is also known as the KK8A-brane. At the same time, we consider its eleven-dimensional uplift, the solution of the 8_{12}^{(1,0)}(1234567z,,8)-brane (REF ). In this case, the linear winding-coordinate dependence is included in \gamma ^{8} = m\...
{ "cite_spans": [] }
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[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
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Physics
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be600ecfb3a1ef07b7bfa3d9dcdfc2f17efa8807
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KK8A and M9 solutions
\end{split}By translating the dual fields into the conventional fields (recall (REF )), we obtain\begin{split} &{\mathrm {d}}s^2 = \Bigl (\frac{c^2+\tau _2^2}{\tau _2}\Bigr )^{1/2}\, \bigl ({\mathrm {d}}x^2_{01\cdots 7}+\tau _2\,{\mathrm {d}}x_{9}^2\bigr ) + \tau _2^{-1}\,\Bigl (\frac{c^2+\tau _2^2}{\tau _2}\Bigr )^{-1...
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10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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0ae64f9ea74cf9fdfd9c3fb9d780b4a50511ead2
subsection
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KK8A and M9 solutions
This is a solution of a deformed type IIA supergravity. The eleven-dimensional uplift corresponds to the bound state of the 8_{12}^{(1,0)}(1\cdots 8,,\text{M})-brane and the 8_{12}^{(1,0)}(1\cdots 7\text{M},,8)-brane, and the corresponding background will be a solution of the \mathrm {SL}(2)-covariant eleven-dimensiona...
{ "cite_spans": [ { "arxiv_id": "", "doi": "", "end": 344, "openalex_id": "", "raw": "P. Meessen and T. Ortín, “An Sl(2,Z) multiplet of nine-dimensional type II supergravity theories,” Nucl. Phys. B 541, 195 (1999) [hep-th/9806120].", "source_ref_id": "9df00eb9eecea1a7634d6298a...
10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.010285042226314545, 0.022248651832342148, -0.03595186769962311, -0.05285962298512459, -0.026506109163165092, 0.00160894519649446, 0.03918692469596863, 0.07184269279241562, 0.03921744227409363, -0.016663599759340286, -0.059116099029779434, 0.043795354664325714, -0.00802660547196865, 0.03...
919faeee643a1b535fe69e4f27028ea6fd15ebbe
subsection
117
130
Conventions
We define the totally antisymmetric delta functions as\delta ^{m_1\cdots m_p}_{n_1\cdots n_p} \equiv \delta ^{[m_1}_{[n_1}\cdots \delta ^{m_p]}_{n_p]} \,,where the antisymmetrization is defined asA_{[m_1\cdots m_n]} \equiv \frac{1}{n!}\,\bigl (A_{m_1\cdots m_n} \pm \text{permutations}\bigr ) \,.We also define the antis...
{ "cite_spans": [] }
10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ -0.020491795614361763, -0.0045240637846291065, -0.032469503581523895, -0.023955414071679115, 0.003784039756283164, -0.039000023156404495, 0.009208339266479015, 0.03857279196381569, 0.052122097462415695, 0.026473021134734154, -0.03344602882862091, -0.022795788943767548, -0.00791138969361782, ...
da68cd6e4432b8f735157d7dd12f88c5f302955e
subsection
118
130
Parameterizations of the generalized metric in EFT
In this appendix, we review the parameterization of the generalized metric in E_{n(n)} EFT (n\le 7). We follow the convention used in .
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10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
[ 0.01051140483468771, 0.02691163681447506, -0.01780378632247448, -0.010091863572597504, -0.013104929588735104, -0.04000131040811539, -0.007101682014763355, -0.012677760794758797, 0.022685715928673744, 0.01225059200078249, -0.026438700035214424, 0.0347837470471859, 0.0009215595782734454, 0.0...
fc17188070e5d23d3a0fb53f9f936d8cecf0bdae
subsection
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M-theory parameterization
When we consider M-theory, we can parameterize the generalized metric \mathcal {M}_{IJ} in terms of the conventional supergravity fields G_{ij}, A_{i_1i_2i_3}, and A_{i_1\cdots i_6} as follows (see , , for earlier works):\begin{split} &\mathcal {M}_{IJ} = (L_6^\mathrm {T}\,L_3^\mathrm {T}\,\hat{\mathcal {M}}\,L_3\,L_6)...
{ "cite_spans": [ { "arxiv_id": "", "doi": "10.1007/jhep02(2012)108", "end": 3471, "openalex_id": "https://openalex.org/W3101545881", "raw": "D. S. Berman, H. Godazgar, M. J. Perry and P. West, “Duality invariant actions and generalised geometry,” JHEP 1202, 108 (2012) [arXiv:1111.04...
10.1007/JHEP09(2018)072
1805.12117
Weaving the Exotic Web
[ "Jose J. Fernandez-Melgarejo", "Tetsuji Kimura", "Yuho Sakatani" ]
[ "hep-th" ]
2,018
en
Physics
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