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7143cd8a4e3a823afd5c20fc860c19f1874e12cb | subsection | 18 | 24 | Effect of | REF (a),
while two electrons occupying the lowest orbital level
do not contribute to the Kondo effect,
the other electron causes the SU(2) Kondo effect
with spin degrees of freedom.
On the other hand,
in the configuration described in Fig. REF (b),
the SU(4) Kondo effect
with spin and orbital degrees of freedom becomes... | {
"cite_spans": []
} | 10.1143/JPSJ.77.094707 | 0807.1780 | Three-orbital Kondo effect in single quantum dot system with plural
electrons | [
"Tomoko Kita",
"Rui Sakano",
"Takuma Ohashi",
"Sei-ichiro Suga"
] | [
"cond-mat.str-el",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
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e7f05eb8a941aad0f5e4facb21dc47c5f3cd858e | subsection | 19 | 24 | With three electrons; | In this subsection,
we study the three-orbital Kondo effect with three electrons
(n_{tot}=3):
The center of the energy levels in eq. (REF ) is
\varepsilon _c = -5U/2.
It is expected that
the Kondo effect occurs for any values of
the level-splitting and the Hund-coupling,
which significantly differs from the case with t... | {
"cite_spans": []
} | 10.1143/JPSJ.77.094707 | 0807.1780 | Three-orbital Kondo effect in single quantum dot system with plural
electrons | [
"Tomoko Kita",
"Rui Sakano",
"Takuma Ohashi",
"Sei-ichiro Suga"
] | [
"cond-mat.str-el",
"cond-mat.mes-hall"
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5a2a4353e68685c4da14edd928915f642ee59f80 | subsection | 20 | 24 | Competition between Hund-coupling and level-splitting | Let us now turn to investigate the effect of the Hund-coupling.
As mentioned before,
the Hund-coupling is competitive to the level-splitting
as seen in the singlet-triplet Kondo effect.
In particular, we consider the orbital configurations described in
Figs. REF (a) and REF (b).
We refer to them as type A and type B in... | {
"cite_spans": []
} | 10.1143/JPSJ.77.094707 | 0807.1780 | Three-orbital Kondo effect in single quantum dot system with plural
electrons | [
"Tomoko Kita",
"Rui Sakano",
"Takuma Ohashi",
"Sei-ichiro Suga"
] | [
"cond-mat.str-el",
"cond-mat.mes-hall"
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e40a491ee7e2987a7bbca385b407f5534120176c | subsection | 21 | 24 | Temperature dependence | We have carried out our analysis by applying the NCA to even lower temperatures,
although this method is valid for temperatures
around and higher than the Kondo temperature.
In this subsection,
we complementally investigate the temperature dependence of transport quantities
in the typical parameter region,
to confirm t... | {
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"doi": "",
"end": 1905,
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"raw": "R. Sakano and N. Kawakami: Phys. Rev. B 73 (2006) 155332.",
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"start": 1743
}
]
} | 10.1143/JPSJ.77.094707 | 0807.1780 | Three-orbital Kondo effect in single quantum dot system with plural
electrons | [
"Tomoko Kita",
"Rui Sakano",
"Takuma Ohashi",
"Sei-ichiro Suga"
] | [
"cond-mat.str-el",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
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4a639fe6bffd457e8e3d86167a4c405f0040eddf | subsection | 22 | 24 | Summary | We have studied the Kondo effect and transport properties
in vertical QD systems with orbital degrees of freedom.
By applying the NCA to the three-orbital Anderson impurity model
with the finite Coulomb interaction and Hund-coupling,
we have investigated
the magnetic-field dependence of transport properties,
the conduc... | {
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{
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"end": 1024,
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"raw": "S. Amaha, T. Hatano, S. Sasaki, T. Kubo, Y. Tokura, and S. Tarucha: presented at The Physical Society of Japan the 61st Annual Meeting, 2006.",
"source_ref_id": "dd1ce3bfde609f3f80836f005bb13... | 10.1143/JPSJ.77.094707 | 0807.1780 | Three-orbital Kondo effect in single quantum dot system with plural
electrons | [
"Tomoko Kita",
"Rui Sakano",
"Takuma Ohashi",
"Sei-ichiro Suga"
] | [
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9532fb259400432a78f33f3ead83c3c5155766cf | subsection | 23 | 24 | Summary | Comparing our results with the exact values, we have discussed
the qualitative behavior at lower temperatures.The similar discussion can be applied to the
multiorbital case which has more than three orbital degrees of freedom.
The Kondo temperature, the unitary limit and
the effective filling contribute significantly t... | {
"cite_spans": []
} | 10.1143/JPSJ.77.094707 | 0807.1780 | Three-orbital Kondo effect in single quantum dot system with plural
electrons | [
"Tomoko Kita",
"Rui Sakano",
"Takuma Ohashi",
"Sei-ichiro Suga"
] | [
"cond-mat.str-el",
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73979dcbe3446c8544b73767a5a5c1ce7a9c6c95 | abstract | 0 | 1 | Abstract | We give an alternative definition of quantum fidelity for two density
operators on qudits in terms of the Hilbert-Schmidt inner product between them
and their purity. It can be regarded as the well-defined operator fidelity for
the two operators and satisfies all Jozsa's four axioms up to a normalization
factor. One de... | {
"cite_spans": []
} | 10.1016/j.physleta.2008.10.083 | 0807.1781 | An alternative quantum fidelity for mixed states of qudits | [
"Xiaoguang Wang",
"Chang-Shui Yu",
"X. X. Yi"
] | [
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41ca072f65cc84f3111853939319d9ca0bc9c4e9 | abstract | 0 | 46 | Abstract | For a one-parameter family of general type hypersurfaces with bases of
holomorphic n-forms, we construct open covers using tropical geometry. We show
that after normalization, each holomorphic n-form is approximately supported on
a unique open component and such a pair approximates a Calabi-Yau hypersurface
together wi... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
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6e391f570abeb7e1a2916f754cc13006eb07422f | subsection | 1 | 46 | Introduction | Calabi-Yau manifolds are Kähler manifolds with zero first Chern
class. By Yau's theorem , they admit Ricci flat Kähler
metrics. They play important roles in String theory as internal
spaces. Up to a scalar multiple, there exists a unique holomorphic
volume form \Omega \in H^{n,0}\left( Y\right) on any Calabi-Yau
manifo... | {
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5336cd97f19f460fa07f26a541cbc85ec04334bf | subsection | 2 | 46 | Introduction | This is not a
connected sum decomposition as different U_{i,t}'s can have large
overlaps. However, it still enables us to have a proper notion of
special Lagrangian fibrations on V_t and study the SYZ
transformation along them.If V_{t} is a family of general type hypersurfaces in
{{\mathbb {C}}{\mathbb {P}}}^{n+1}, i.e... | {
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ee728ba9540344c75dc7f40997645cf940ff4f70 | subsection | 3 | 46 | Introduction | In this article, we prove the
followingTheorem (Main Theorem)
For any positive integers n and d with d\ge n+2, there exists
a family of smooth hypersurfaces V_t\subset {\mathbb {C}}{\mathbb {P}}^{n+1} of degree
d such that V_t can be written asV_t=\bigcup _{i\in \triangle _{d,\mathbb {Z}}^0} U_{i,t}where U_{i,t} is a ... | {
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4d7b76b893c692960c5d8688128f04d040565458 | subsection | 4 | 46 | Introduction | (In here, we abused the notion of
“decomposition" since the open sets U_{i,t} that we obtained in
the “decomposition" do overlap even as t\rightarrow +\infty .) Therefore we
can speak of special Lagrangian submanifolds in V_{t}.Definition 1.1 Let L_{t}\subset V_{t} be a smooth family of Lagrangian
submanifolds. We call... | {
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97282afffb886e2ee9a8d8e662f7d8be605d3160 | subsection | 5 | 46 | Amoebas and Viro's patchworking | Let V^o be a smooth hypersurface in (*)^{n+1}\subset {\mathbb {C}}{\mathbb {P}}^{n+1}
or other toric varieties defined by a Laurent polynomialf(z)=\sum _j{a_j}z^j,where j=(j_1,\ldots ,j_{n+1})\in \mathbb {Z}^{n+1} are multi-indices. Recall
that the Newton polyhedron \triangle \subset \mathbb {R}^{n+1} of f,
or of V^o, ... | {
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0a9d1ecc26b182a6d6984c7716b4764f331a27ec | subsection | 6 | 46 | Amoebas and Viro's patchworking | It is then easy to see
that the field K can also be represented by the field of Puiseux
series\tilde{b}=\sum _{p\in \tilde{\Lambda _{{b}}}}\tilde{b}_pt^pwith \max \tilde{\Lambda }_p<+\infty and valuation
\mbox{val}_K(\tilde{b})=-\max \tilde{\Lambda }_{{b}}.Since e^{-\mbox{val}_K} defines a norm \Vert \cdot \Vert _K on ... | {
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e596852bcd58b2f0063a6e6844b313c8d13ca1e4 | subsection | 7 | 46 | Amoebas and Viro's patchworking | In
particular, the interior of a top dimensional face of \Pi _v is
given by{F}(j^{(1)},j^{(2)})=\lbrace
x\in \mathbb {R}^{n+1}\,:\,l_{v,j^{(1)}}(x)=l_{v,j^{(2)}}(x)>l_{v,j}(x),\,
\forall \, j\ne j^{(1)},\, j^{(2)}\rbrace .It was proved in
that \Pi _v is a balanced polyhedral complex dual to
certain lattice subdivisio... | {
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05195cf6c380afac19b2851109a8ba52e583ccb2 | subsection | 8 | 46 | Maximal dual complex | As we mentioned, it was proved in that \Pi _v is a
balanced polyhedral complex dual to certain lattice subdivision of
the convex hull \triangle of A in \mathbb {R}^{n+1}. In general, any
n-dimensional balanced polyhedral complex \Pi in \mathbb {R}^{n+1}
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0d61594381b0f76248735c4aa251f6a72f5d8023 | subsection | 9 | 46 | Pairs-of-pants decomposition and stratified fibration | In this subsection, we state the pairs-of-pants decomposition and
existence of stratified fibration theorem of Mikhalkin
which is the main ingredient of the proof of our results. We start
with the definition of pair-of-pants and stratified fibration given
in .As in , we denote by \mathcal {H} a union of n+2 generic
hy... | {
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b5caadff5fa11e5952ae4999b884bb42b32d70c5 | subsection | 10 | 46 | Pairs-of-pants decomposition and stratified fibration | Then for every maximal dual \triangle _d-complex \Pi , there
exists a stratified n-fibration \lambda :\, V\rightarrow \Pi
satisfyingthe induced map \lambda ^*: H^n(\Pi , \mathbb {Z})\approx \mathbb {Z}^{p_g} \rightarrow H^n(V,\mathbb {Z}) is
injective, where p_g=h^{n,0}(V) is the geometric genus of V;
for each primit... | {
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5932c535060f7bd38e7c05d12224b7d5184526ae | subsection | 11 | 46 | Key lemma | To prove the main theorem, we need to show the existence of a real
valued function v:\triangle _{d,\mathbb {Z}}\rightarrow \mathbb {R}, where
\triangle _{d,\mathbb {Z}}=\triangle _{d}\cap \mathbb {Z}^{n+1} and d\ge n+2, such
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94bfbd36a9e84bbcf663bc26513cf1d1c4282f2b | subsection | 12 | 46 | Proof of the main theorem | In this section, we give the proof of the main theorem. Recall that
we are free to use any hypersurface defined by a homogeneous
polynomial of degree d of n+1 variables to replace V in order
to describe V as a smooth manifold or as a symplectic manifold.
The idea of tropical geometry leads us to consider the submanifol... | {
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f09eeb016ba91b2fd83b57513de418b9359db1e0 | subsection | 13 | 46 | Proof of the main theorem | Recall that the set of interior lattice
points of \triangle _d is exactly equal to p_g=\left(
\begin{array}{c} d-1 \\n+1 \end{array} \right) (see for instance ) and note that
{F}(i,j)\ne \emptyset only when i and j is connected by
an edge in the lattice subdivision of \triangle _d dual to \Pi _v.
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51af78b792f186f0f3a7536e9e1026ad14858d38 | subsection | 14 | 46 | Proof of the main theorem | Then for all t>0, there exists a
basis \lbrace \Omega _{i,t}\rbrace _{i\in \triangle _{d,\mathbb {Z}}^0} of H^{n,0}(V_t),
and open subsets {U}^{\wedge }_{i,t} \subset V_t\cap (*)^{n+1}
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e68795aab597c0c64cdfd8627eb47d18b299ff39 | subsection | 15 | 46 | Proof of the main theorem | This proves
the first statement.
[Figure: NO_CAPTION]Figure 6: The construction of the neighborhood
{C}^{\wedge }_{i,t}.To see the other two statements, we use the well-known fact that on
the variety V_{t}, the Poincaré residues of
f_t^{-1}dz_1\wedge \cdots \wedge dz_{n+1} define a holomorphic
n-form on V_t; and all el... | {
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647f2ce2032dad76813702291cbe22e9300f5bc7 | subsection | 16 | 46 | Proof of the main theorem | Explicitly, in the region with f_{z_\alpha }\ne 0,\Omega _i & = &
(-1)^{\alpha -1}(\log t)^{-n}\frac{t^{-v(i)}z^{i}}{z_1\cdots z_{n+1}}\frac{dz_1\wedge \cdots \widehat{dz_\alpha }\cdots \wedge dz_{n+1}}{f_{z_\alpha }} \\
& = & (-1)^{\alpha -1}(\log t)^{-n}\frac{t^{-v(i)}z^{i}}{\sum _j
j_\alpha t^{-v(j)}z^j}
\frac{dz_1}... | {
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0.07244873046875,
0.188720703125,
0.0399169921875,
0.149169921875,
0.0692138671875,
0.2413330078125,
0.01025390625,
0.1273193359375,
0.1138916015625,
... | |
f088d445ce57f6f7ac8908e4a377a7c2998a5ad2 | subsection | 17 | 46 | Proof of the main theorem | Therefore for any compact subset
R\Subset \operatorname{Int}({F}(i,j^{(1)})) the terms
t^{-v({i})}z^{{i}} and t^{-v(j^{(1)})}z^{j^{(1)}} dominate other
terms of f_t in a neighborhood of \lambda ^{-1}(R)\subset V_t\cap (*)^{n+1} in (*)^{n+1} as t\rightarrow +\infty .For each \alpha \in \lbrace 1,\ldots ,n+1\rbrace , the... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
228072,
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34aa3cd16a2fcd42fcd357d184cf8298703eddb2 | subsection | 18 | 46 | Proof of the main theorem | Putting the above expression
into the definition of \Omega _i and using f=0 on V_t, we have\Omega _i = (\log t)^{-n} \left[
\frac{(-1)^{\alpha -1}t^{-v(i)}z^{i}}{(j^{(1)}_{\alpha }-{i}_\alpha )
t^{-v(j^{(1)})}z^{j^{(1)}}+ \cdots } \right]
\frac{dz_1}{z_1}\wedge \cdots \widehat{\left(\frac{dz_\alpha }{z_\alpha }\right)}... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
36917,
125195,
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0.08154296875,
0.... | |
7bf2fd10d9a3bc3de3ec37227b170f3d0efdb87d | subsection | 19 | 46 | Proof of the main theorem | Denote j^{(0)}=i and
\zeta _p=t^{-v(j^{(p)})}z^{j^{(p)}} for p=0,\ldots ,n+1. Then0=f(z)=\sum _{p=0}^{n+1} \zeta _p + \cdots ,andz_{\alpha }f_{z_\alpha }&=&\sum _j j_\alpha t^{-v(j)}z^j\\
&=&\sum _{p=0}^{n+1}j^{(p)}_{\alpha } \zeta _p + \cdots \\
&=& j^{(0)}_{\alpha }\left( \sum _{p=0}^{n+1} \zeta _p \right) +
\sum _{p... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
262,
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0.0... | |
29474afba393f0faec5ed92b47fcef154de955e3 | subsection | 20 | 46 | Proof of the main theorem | We claim that for any b, there exists \alpha \in \lbrace 1,\ldots ,n+1\rbrace such that\lim _{t\rightarrow +\infty }\sum _{p=1}^{n+1}(j^{(p)}_{\alpha }-j^{(0)}_\alpha )
\frac{\zeta _{p}}{\zeta _{0}}\ne 0.In fact, if it is not true, then by taking t\rightarrow +\infty , we have for all \alpha ,\lim _{t\rightarrow +\inft... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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326aa3269bc47ba1e0505b2a309aa894bf0a864c | subsection | 21 | 46 | Proof of the main theorem | This completes the
proof of the second statement.Finally for the last statement of the theorem, we observe that on
any compact subset B\subset {\mathbb {C}}{\mathbb {P}}^{n+1}\setminus {U}^{\wedge }_{i,t},
t^{-v(i)}z^{i} is no longer a dominating term near V_t\cap B and
hence \Omega _i \rightarrow 0 locally in B as t\r... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 516,
"openalex_id": "",
"raw": "Mikhalkin, G., Tropical Geometry and Amoebas, Preprint, 2003.",
"source_ref_id": "8cfdf99dc91572d349c5b308e1c0124cdcfff87a",
"start": 423
}
]
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
3293,
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0.138427734... | |
9ae3b6a2a2c39432fd946692fc74e71d3f853df6 | subsection | 22 | 46 | Proof of the main theorem | Then for all t>0, there exists a
basis \lbrace \Omega _{i,t}\rbrace _{i\in \triangle _{d,\mathbb {Z}}^0} of H^{n,0}(V_t),
and open subsets {U}_{i,t} \subset V_t such that
for each i\in \triangle _{d,\mathbb {Z}}^0,\mbox{Log}_t({U}_{i,t}) tends to an n-cycle C_i such that \Pi _v =\bigcup _{i\in \triangle _{d,\mathbb {Z}... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
47009,
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0.0849609375,
0.1153564453125,
0.00210... | |
e8d24042a518f6ac6d96c68f40e159003acf7618 | subsection | 23 | 46 | Proof of the main theorem | We defineC_i=C_i^{\wedge }\bigcup \left( \bigcup _{s\in \Lambda _i} \overline{\mathcal {U}_{s}} \right),where \mathcal {U}_s is the primitive piece dual to the simplex \sigma _s.
[Figure: NO_CAPTION]Figure 7: Illustration of the sets C^{\wedge }_{i}
and C_i.Then we clearly have\Pi _v=\bigcup _{i\in \triangle _{d,\mathb... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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0.09375,
0.0775146484375,
0.060180664... | |
21ee7399308e3fcba8580452b97deffba9587c6b | subsection | 24 | 46 | Proof of the main theorem | Recall
that the lemma REF implies that the subdivision
corresponding to v restricts to a lattice subdivision of
i-{\i }+\triangle _{n+2}. Consider the truncated polynomial
f_{i,t}=\displaystyle \sum _{j \in i-{\i }+\triangle _{n+2}}
t^{-v(j)}z^j. This truncated polynomial f_{i,t} factorizes asf_{i,t}= z^{i-{\i }} \sum ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1175,
"openalex_id": "",
"raw": "Mikhalkin, G., Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology 43 (2004) 1035-1065.",
"source_ref_id": "4b3e6df8a9e231d9e6090ac237444da5d7c86f38",
"start... | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
85763,
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6156fa0614eba3d6f7b5553c6199266b619f9cbd | subsection | 25 | 46 | Proof of the main theorem | This proves the first statement.To see the other two statements, we observe that the limiting
behavior of \Omega _{i,t} shows that \Omega _{i,t} is close to the
corresponding holomorphic n-form \Omega _{Y_{i,t}} of the
Calabi-Yau hypersurface
\lbrace {f}^{CY}_{i,t}=0\rbrace =Y_{i,t}\subset {\mathbb {C}}{\mathbb {P}}^{n... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
3293,
23534,
7,
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0.0031433... | |
f346bc6db1a8d3e23e664a1e90b56f2d2ba2b250 | subsection | 26 | 46 | Proof of the main theorem | In fact, since
{f}^{CY}_{i,t}=0 on the hypersurface \lbrace f_{i,t}=0\rbrace , we have\Omega _{Y_{i,t}} & = & (\log t)^{-n} \left[
\frac{(-1)^{\alpha -1}t^{-v(i)}z^{\i }}{z_\alpha (
{f}^{CY}_{i,t})_{z_{\alpha }}} \right]
\frac{dz_1}{z_1}\wedge \cdots \widehat{\left(\frac{dz_\alpha }{z_\alpha }\right)}
\cdots \wedge \fr... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
15824,
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4,
18,
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20e9abe4afeb84336b25fc2a184177a09ae265d3 | subsection | 27 | 46 | Proof of the main theorem | In a neighborhood of
U_{i,t}\cap \left({\mathbb {C}}{\mathbb {P}}^{n+1}\setminus (*)^{n+1}\right), we
consider those open subsets correspond to top dimensional faces. In
these open subsets, the polynomial f and f_{i,t} are dominated
by exactly two terms t^{j^{1}}z^{j^{(1)}} and
t^{j^{2}}z^{j^{(2)}}. Then\frac{\Omega _{... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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ab3e474920a7887b4385536c4ef21a9f3f9a6a7c | subsection | 28 | 46 | Proof of the main theorem | Since
\Omega _{Y_{i,t}} is the holomorphic volume of the Calabi-Yau
hypersurface Y_{i,t}, it is non-vanishing and hence \Omega _{i,t}
is also non-vanishing on the whole U_{i,t}.Finally, as U_{i,t}\supset {U}^{\wedge }_{i,t}, the last statement follows immediately from the last statement of the theorem REF
This complet... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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5027f9dd12c0e273c120b934c6457700eb7957fc | subsection | 29 | 46 | Asymptotically special Lagrangian fibers | From the fibration \lambda given in , for each n-cell
e of \Pi _v, there exists a point x\in e
such that the fiber \lambda ^{-1}(x) is a Lagrangian n-torus
n\subset V which is actually given by \lbrace z\in V_t: \mbox{Log}_t|z|=x\rbrace .
Therefore, when restricted to this fiber\left.\Omega _i\right|_{\lambda ^{-1}(x)}... | {
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{
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"end": 239,
"openalex_id": "",
"raw": "Mikhalkin, G., Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology 43 (2004) 1035-1065.",
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"start"... | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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0... | |
7d0806003046994b54b5fe7b3cc1b5e1fc201c05 | subsection | 30 | 46 | Hypersurfaces in other toric varieties; the case of curves | It is clear from the works of Mikhalkin , our result can
be modified to include other toric varieties such as
{\mathbb {C}}{\mathbb {P}}^m\times {\mathbb {C}}{\mathbb {P}}^n. In particular, if we apply our method to curves
in {\mathbb {C}}{\mathbb {P}}^1\times {\mathbb {C}}{\mathbb {P}}^1 instead of {\mathbb {C}}{\math... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 174,
"openalex_id": "",
"raw": "Mikhalkin, G., Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology 43 (2004) 1035-1065.",
"source_ref_id": "4b3e6df8a9e231d9e6090ac237444da5d7c86f38",
"start"... | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
34735,
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54f520f7f1ed9a29b38560a6af7c2ddc333b0dd6 | subsection | 31 | 46 | Hypersurfaces in other toric varieties; the case of curves | In summary, we haveTheorem 3.4
For any integer g\ge 1, there is a family of smooth genus g
curves V_t of bi-degree (g+1,2) in {\mathbb {C}}{\mathbb {P}}^1\times {\mathbb {C}}{\mathbb {P}}^1, such that
V_t can be written asV_t=\bigcup _{i=1}^g U_{i,t}where \lbrace U_{i,t}\rbrace is a family of closed subsets U_{i,t}\su... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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0.0... | |
ab93b8673fd3b6e9c924b7d31aafcab1d637fbec | subsection | 32 | 46 | Hypersurfaces in other toric varieties; the case of curves | In fact, one shows
that there exists a function v:\triangle _{\mathbb {Z}}\rightarrow \mathbb {R} such that
\Pi _v is a maximal dual complex of \triangle giving the required
subdivision.
[Figure: NO_CAPTION]Figure 9: A maximal dual \triangle complex with the required properties.As in the proof of the main theorem, we c... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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ee11bdfa2d4363e478196142934d84eb4b8fd85a | subsection | 33 | 46 | Proof of the key lemma | In this section, we prove the lemma REF concerning the dual
complex \Pi _v given by the function v:\triangle _{d,\mathbb {Z}}\rightarrow \mathbb {R} defined byv(j)=\sum _{\alpha =1}^{n+1} j_\alpha ^2+\left( \sum _{\alpha =1}^{n+1}
j_\alpha \right)^2for j=(j_1,\ldots ,j_{n+1})\in \triangle _{d,\mathbb {Z}}. To
simplify ... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
903,
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c66c614527756d479f5540396be616109164250e | subsection | 34 | 46 | Proof of the key lemma | By assumption, j\ne \pm e_\alpha , e_i-e_j, we have the
following strict inequalities from the condition of the lemma{\left\lbrace \begin{array}{ll}
\langle i\pm e_\alpha ,x \rangle -v(i\pm e_\alpha ) &< \langle i,x
\rangle -v(i)
\\
\langle i+e_\beta -e_\alpha ,x \rangle -v(i+e_\beta -e_\alpha ) &<
\langle i,x \rangle ... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
3311,
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0.13366... | |
48d278c74588b10890b3168275aad2ad037f5211 | subsection | 35 | 46 | Proof of the key lemma | \end{array}\right.}Therefore,{\left\lbrace \begin{array}{ll}
|j_\alpha +j_0|<2,& \forall \,\alpha =1,\ldots , n+1\\
|j_\beta -j_\alpha |<2,& \forall \, \beta \ne \alpha =1,\ldots , n+1.
\end{array}\right.}As j_\beta are integers, the first inequality above implies for
all \alpha =1,\ldots ,n+1,-1 \le j_\alpha +j_0 \le ... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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0.2... | |
a3a97821841c445cadf481f6ae4a6477e86c1fdc | subsection | 36 | 46 | Proof of the key lemma | \end{array}\right.}And for those \alpha with i_\alpha +j_\alpha =0, we only have the
one-sided inequalityx_\alpha -2(i_\alpha +j_\alpha +i_0+j_0)<2.Hence for \alpha with i_\alpha +j_\alpha \ge 1, we still have|j_\alpha +j_0|<2.However, for \alpha with i_\alpha +j_\alpha =0, we only have-2<i_\alpha +j_0.Since i+j\in \pa... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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16414529d71bda9bd3ea2f794d2105fa7493b6c1 | subsection | 37 | 46 | Proof of the key lemma | Then for all \alpha ,
i+j+e_\alpha =e_\alpha \in \triangle _{d,\mathbb {Z}}. The condition of
the lemma implies\langle i+j+e_\alpha , x \rangle -v(i+j+e_\alpha )<\langle i+j,
x\rangle -v(i+j).So x_\alpha <v(e_\alpha )=2 for all \alpha . On the other hand, the
condition of the lemma gives the equality\langle i+j, x \ran... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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3d13bd80b197646eea2d2ca462711711f1535cf0 | subsection | 38 | 46 | Proof of the key lemma | Similar argument impliesx_\gamma -x_\alpha -2(i_\gamma +j_\gamma -i_\alpha -j_\alpha )<2provided i_\alpha +j_\alpha \ge 1 and \gamma \ne \alpha .The second inequality together with|x_\gamma -x_\alpha -2(i_\gamma -i_\alpha )|<2imply-2<x_\gamma -x_\alpha -2(i_\gamma -i_\alpha )<2+2(j_\gamma -j_\alpha ).That isj_\alpha <2... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
209683,
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... | |
398d8f8d9e97368e1b84e9bd7579c8943ff65efd | subsection | 39 | 46 | Proof of the key lemma | This proved the Case 2 and
the proof of Step 3 is completed.Step 4: Either j\in \lbrace y\in \mathbb {R}^{n+1}:y_\beta =0\rbrace \cap \partial \triangle _d\cap \mathbb {Z}^{n+1} for
some \beta and i+j \in \lbrace y\in \mathbb {R}^{n+1}:y_\alpha =0\rbrace \cap \partial \triangle _d\cap \mathbb {Z}^{n+1} for
some \alpha ... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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fcd1e1cdd1f0b1a4185171fbfd240582fdae7670 | subsection | 40 | 46 | Proof of the key lemma | Then i+e_\alpha \in \triangle _{d,\mathbb {Z}} and
hencex_\alpha -2(i_\alpha +i_0)<2\quad \forall \,\alpha .Since we also have i+j-e_\alpha \in \triangle _{d,\mathbb {Z}}, we get-2<x_\alpha -2(i_\alpha +j_\alpha +i_0+j_0).These implyj_\alpha +j_0<2,\quad \forall \, \alpha .Summing over \alpha implies j_0<2. So j_0\le 1... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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c2d4ea62adcc884003091646ac6ad0d5647633c3 | subsection | 41 | 46 | Proof of the key lemma | Together with
j_0=0, we conclude that j=0 which is a contradiction.So we must have j_\gamma \le 0 for all \gamma with i_\gamma \le 1. Then j_\alpha -j_\gamma <2 impliesj_\alpha <2,\quad \forall \, \alpha \mbox{ with }i_\alpha =0.Thereforej_\alpha \le 1,\quad \forall \,\alpha \mbox{ with }i_\alpha =0.On the other hand, ... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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bd000e7ce8fc3e192794497a8e96f9bb5ef014dd | subsection | 42 | 46 | Proof of the key lemma | This proves the
Step 5.Completion of the proof of the lemma: By Step 5, if
there exists x\in \mathbb {R}^{n+1} satisfying the condition of the lemma,
then i and i+j belong to \lbrace y\in \mathbb {R}^{n+1}\,:\,
y_\beta =0\rbrace \cap \triangle _{d,\mathbb {Z}} for some \beta . This
reduces the argument to one lower dim... | {
"cite_spans": []
} | 0807.1784 | Calabi-Yau components in general type hypersurfaces | [
"Naichung Conan Leung",
"Tom Y. H. Wan"
] | [
"math.AG",
"math.SG"
] | 2,008 | en | Mathematics | [
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7aa1a988c02c3df003988b8ec57690febfce9dce | subsection | 43 | 46 | Proof of the key lemma | Since the proposition
is clearly true for 1-dimension, induction implies the lemma holds.Lemma 4.2
For any i\in \triangle _{d,\mathbb {Z}}, there exists at most n+1
elements j_{\gamma }\in \lbrace \pm e_\beta , e_\beta -e_\alpha \rbrace _{\beta \ne \alpha } with j_{\gamma _1}+j_{\gamma _2}\ne 0 such that there
exists ... | {
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d886d6880650e15d10ffe20840b38393c5b3b656 | subsection | 44 | 46 | Proof of the key lemma | Therefore, each \beta =1,\ldots ,
n+1 can appeared once in the set \lbrace j_{\gamma }\rbrace and this
completes the proof of the lemma.Proof of the key lemma REF : It is clear from
the lemmas REF and REF , the balanced polyhedral
complex \Pi _v corresponding to
v(j)=\displaystyle \sum _{\beta =0}^{n+1}j_\beta ^2 is a ... | {
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1fb871d26a645dc78ab4e225016937a42f78c32b | subsection | 45 | 46 | Appendix: Definition of balanced polyhedral complex | In this appendix, we state the Mikhalkin's definition of
a balanced polyhedral complex for reader's reference.Definition 5.1 A subset \Pi \in \mathbb {R}^{n+1} is called a rational
polyhedral complex if it can be represented as a finite union of
closed convex polyhedra (possibly semi-infinite) called cells
in \mathbb {... | {
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8609cf60d7ca9acb07505d40c29d85372a0196d5 | abstract | 0 | 26 | Abstract | The motion of a particle near the Reissner-Nordstrom black hole horizon is
described by conformal mechanics. In this paper we present an extended
one-dimensional analysis of the N=4 superconformal mechanics coupled to n
copies of N=8, d=1 vector supermultiplets. The constructed system possesses a
special Kahler geometr... | {
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} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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8ad22834022ae0aab0a87f79a24ad07acaf24924 | subsection | 1 | 26 | Introduction | Recently, the supersymmetric one dimensional theories appeared in the two different but related four-dimensional systems.
Firstly, in it was established connection between black holes and conformal mechanics .
Geodesic motion of a particle near the horizon of an extreme Reissner-Nordström black hole was shown to be re... | {
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487ef12f12d02f04ce2c40e871c26f757fd1557c | subsection | 2 | 26 | N=8 vector supermultiplet and BH potential | In this Section we demonstrate how the bosonic sector of the most general action for n-vector N=8, d=1 supermultiplets
reproduces the main part of the BH action , (with the supergravity sector being switched off). The constructed action
contains the effective “black hole potential” initially introduced in . We also exp... | {
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609063a5d586de1bbc786650b5b76903f0a00990 | subsection | 3 | 26 | N=8 vector supermultiplet and BH potential | All relevant notations and definitions are given in appendix A.This action is notable for the fact that its bosonic part contains the well-known effective black hole potential \displaystyle S_{bos}=\int dt\left[ \rule {0pt}{1.2em} M_{AB} {\dot{z}}{}^A {\dot{\bar{z}}}{}^B - V(p,q,z,\bar{z})\right],\quad V=\frac{1}{16}\l... | {
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af2d6a6cfcc91df8c4f082e8c9d03057eb4f7222 | subsection | 4 | 26 | N=8 vector supermultiplet and BH potential | The auxiliary components X^A and Y^A of the vector supermultiplet are not completely independent, but subjected to the constraints (REF ):\frac{\partial }{\partial t} \left( X^A-{\overline{\strut Y}}\,{}^A \right) = 0,while the rest four auxiliary bosonic components Y^{a\alpha } are expressed, as a consequence of their... | {
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dcc8ab09c042bc13dfe2e8ae2d55b15b2e9df437 | subsection | 5 | 26 | N=8 vector supermultiplet and BH potential | Substituting all these into the action (REF ) we getS_{bos} = \int dt \left[ M_{AB}\;{\dot{z}}{}^A {\dot{\bar{z}}}{}^B +\frac{1}{16} M_{AB}\left( {\dot{\Upsilon }}{}^A {\dot{\Upsilon }}{}^B -p^A p^B +c^A c^B\right)
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4df2df228d99e2fcce9f0ff72d8fd7aa4ff0be37 | subsection | 6 | 26 | The vector supermultiplet in | The simplest way to introduce the interaction with the N=4 conformal supermultiplet is to use N=4 superfields.
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} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
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728f7afb1dde8d363ea9bed246ab7078ee0bcea5 | subsection | 7 | 26 | The vector supermultiplet in | Therefore, all components of the vector supermultiplets are contained
in the N=4 superfields u and \phi depending on \theta _a-i\bar{\vartheta }_a and \bar{\theta }{}^a-i\vartheta ^a only:u=U\rule [-0.5em]{0.4pt}{1.6em}_{\,\vartheta =i\bar{\theta },\bar{\vartheta }=i\theta }, \qquad \phi =\Phi \rule [-0.5em]{0.4pt}{1.6... | {
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4bc616179e249eb29bf95c6bfbc7cb63ef90f033 | subsection | 8 | 26 | The vector supermultiplet in | In the next
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c5a2aee61899f3ffb75a6298bee185437a45d4f8 | subsection | 9 | 26 | Maintaining N=4 superconformal symmetry | In this Section we are going to couple the effective black hole action (REF ) to the N=4 superconformal multiplet.
In one dimension the most general superconformal group is D(2,1;\alpha ) one . Here we restrict
our consideration by the special case with \alpha =-1 which corresponds to SU(1,1|2) symmetry. This superconf... | {
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"S. Krivonos",
"A. Shcherbakov",
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fc9b2d642c18bbdcdaf72213b467c55dcb51bc85 | subsection | 10 | 26 | Maintaining N=4 superconformal symmetry | Therefore, to maintain SU(1,1|2) invariance, one has to introduce the super-dilaton — N=4, d=1 superfield \tilde{u} which transforms as follows\delta {\tilde{u}} = \partial _t E.It is known for a long time that the super-dilaton has to be further constrained by the conditionsD^2 Y = {\overline{\strut D}}{}{}^2 Y = \le... | {
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} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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bd9c3f194fafea0801beccb22e20522dcfa11bac | subsection | 11 | 26 | Maintaining N=4 superconformal symmetry | Therefore, the superconformally invariant
black hole action readsS=-\int dt d^2 \theta d^2 \bar{\theta }\;Y\;\left[ \log {Y}+ {\cal F}\left( \frac{u^A}{Y}+i\phi ^A \right) +
\overline{\strut \cal F}\left(\frac{u^A}{Y}-i\phi ^A\right)\right],where the N=4 superfields are constrained by the conditions (REF ),(REF ) and (... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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a24e4f145e08319886c508662c7d26b7f0b99fc3 | subsection | 12 | 26 | Field content of the supersymmetric black hole action | To find the components action one has to integrate over the Grassmann variables in the superfield action (REF ), remove the auxiliary components
through their equations of motion and perform the dualization in a way discussed in the previous sections. Before presenting the component
action let us define the physical bo... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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b70d40e3ae7f0b4485a174ca73a8f54f68ee4f06 | subsection | 13 | 26 | Field content of the supersymmetric black hole action | Being integrated over the Grassmann variables, the expression (REF ) acquires the following form\begin{array}{l}
\displaystyle S = \int dt \left[
\frac{1}{y}\, {\dot{y}}{}^2 + y M_{AB} {\dot{z}}{}^A \dot{\bar{z}}{}^B - \frac{1}{y}\, V(p,q,z,\bar{z})
\right.\\
\displaystyle \phantom{\displaystyle S = \int dt \left[ \rig... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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cbc120ce681e8ff10d9bde656ed294e336fd2308 | subsection | 14 | 26 | Field content of the supersymmetric black hole action | The dots stand for four-fermionic terms; they do not depend on the charges p^A, q_A and since their explicit form is not too
illuminated, they are written down only in the Hamiltonian.The explicit form of the on-shell action (REF ) together with the N=4 supersymmetry transformations (REF ), (REF ) provides all ingredie... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
"hep-th"
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9514d5ea3df6d00e942808102d5f6e2f7f05b489 | subsection | 15 | 26 | Field content of the supersymmetric black hole action | The rest of the calculations goes straightforwardly, so we omit all details and present the final results.The non-vanishing Dirac brackets between the canonical variables read&& \left\lbrace y, {\cal P}_y\right\rbrace =1, \; \left\lbrace z^A, {\cal P}_B\right\rbrace =\delta ^A_B,\; \left\lbrace {\bar{z}}{}^A,{\bar{{\ca... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
"hep-th"
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e24dddbcadbdc33024c4b210ac9da1b743e8db8a | subsection | 16 | 26 | Field content of the supersymmetric black hole action | \end{array}The supercharges \mathbb {Q} form N=4 superalgebra\left\lbrace {\mathbb {Q}}^a ,\bar{\mathbb {Q}}_b\right\rbrace =2i\delta ^a_b {\mathbb {H}}, \qquad \left\lbrace {\mathbb {Q}}^a ,{\mathbb {Q}}_b\right\rbrace = \left\lbrace \bar{\mathbb {Q}}^a ,\bar{\mathbb {Q}}_b\right\rbrace
= \left\lbrace {\mathbb {H}}, ... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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851f3f44194c248a307f7fcc703ab7376e5ab468 | subsection | 17 | 26 | Field content of the supersymmetric black hole action | \end{array}The highlighted structure of the supercharges {\mathbb {Q}}^a,\bar{\mathbb {Q}}_a is not accidental. | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
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7c2dab63b043768437b300f76e2b90f3ab6ad08c | subsection | 18 | 26 | Field content of the supersymmetric black hole action | One may check that each
set of the sub-supercharges Q^a,{\bar{Q}}_b, {\cal Q}^a,\bar{\cal Q}_b and {\cal S}^a,\bar{\cal S}_b independently forms N=4 superalgebra\left\lbrace Q^a,{\bar{Q}}_b\right\rbrace =2i\delta ^a_b H, \quad \left\lbrace {\cal Q}^a,{\bar{\cal Q}}_b\right\rbrace =2i\delta ^a_b{\cal H}, \quad \left\lbr... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
"hep-th"
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7cf016eb8a4e893ad36cc899b99a255266b57ff4 | subsection | 19 | 26 | Field content of the supersymmetric black hole action | \end{array}As it was mentioned above, the supercharges Q^a,{\bar{Q}}_b are recognized as the supercharges of one dimensional N=4 superconformal
mechanics , , while the mutually anticommuting supercharges {\cal Q}^a and {\cal S}^a span N=8 superalgebra with vanishing central charge , . Thus, coupling of the vector super... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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"hep-th"
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30961a8d493d4cf119c4d353cee42977b528b1a4 | subsection | 20 | 26 | Black hole potential modification | From the point of view of the superconformal group SU(1,1|2), the superconformal multiplet is defined as an exponential of the
dilaton superfield \tilde{u}. The covariance with respect to the superconformal transformations fixes the irreducibility constraints to
be (REF ). Really speaking, these constraints may be slig... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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"hep-th"
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25322161bab5c28f295e49418c54d2d65ae249e1 | subsection | 21 | 26 | Black hole potential modification | The dualization goes the same way as it
is described in the previous section: one should declare the auxiliary field X^A be a constant (again, due to U(1) arguing, it has to
be an imaginary one), while the field Y^A be split on the real and imaginary partsX^A = i p^A,\quad {\overline{\strut X}}{}^A = - i p^A, \quad Y^A... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
"S. Bellucci",
"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
] | [
"hep-th"
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ff06dcb0d0d68fcfafcbcd51f09e6ae27cad5b92 | subsection | 22 | 26 | Conclusion | In this paper we analyzed a system constructed by coupling of n-copies of N=8, d=1 vector supermultiplets to N=4 superconformal one. The N=4 superconformal symmetry uniquely fixes the resulting action. We demonstrated that
the electric and magnetic charges, presenting in the “effective black hole” action appear as a r... | {
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"S. Krivonos",
"A. Shcherbakov",
"A. Sutulin"
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5148781d2e5c4d3e255a130b059cba253d94f1c5 | subsection | 23 | 26 | Appendix | The natural framework to describe N=8 vector supermultiplet is the N=8, d=1 superspace \mathbb {R}^{1|8}\mathbb {R}^{1|8}=(t,\theta ^{ia},\vartheta ^{i\alpha })\,,\qquad \left(\theta ^{ia}\right)^\dagger =\theta _{ia}\,,\qquad \left(\vartheta ^{i\alpha }\right)^\dagger =\vartheta _{i\alpha }\,,where i,\,a,\,\alpha =1,\... | {
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} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
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b45ec65cb1a6cd7b169defe3f641823748cc16b6 | subsection | 24 | 26 | Appendix | SU(2) metric is given by the skew-symmetric tensor\epsilon _{ij} \epsilon ^{jk}=\delta _i^k,\qquad \epsilon _{12} = \epsilon ^{21} =1.In superspace \mathbb {R}^{1|8} we define covariant spinor derivatives satisfying the following superalgebra\left\lbrace D^{ia},D^{jb}\right\rbrace =2i\epsilon ^{ij}\epsilon ^{ab}\partia... | {
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} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
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145f60fa94a0425b9c3bebcb1c1a7d55e044235a | subsection | 25 | 26 | Appendix | The bosonic auxiliary components X and Y are subjected, in virtue of (REF ), to the additional constraints\frac{\partial }{\partial t} \left( X-{{\overline{\strut Y}}\,{}}\right)=0,\quad \frac{\partial }{\partial t} \left( {{\overline{\strut X}}{}}- Y\right)=0.Simple component counting gives that we have two physical b... | {
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} | 10.1103/PhysRevD.78.125001 | 0807.1785 | N=4 Superconformal Mechanics and Black Holes | [
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faae800e467349fda7d1f98eb6cfd74804fc5844 | abstract | 0 | 19 | Abstract | Aims: The TeV BL Lac object Markarian 501 is a complex, core dominated radio
source, with a one sided, twisting jet on parsec scales. In the present work,
we attempt to extend our understanding of the source physics to regions of the
radio jet which have not been accessed before.
Methods: We present new observations o... | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
"M. Giroletti",
"G. Giovannini",
"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
"M. Chiaberge",
"P. G. Edwards"
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24ddc989cc35fb2a4e4f23a723155218d35be8c9 | subsection | 1 | 19 | INTRODUCTION | The study of extragalactic radio jets is an important area in astrophysics. In
radio loud sources, jets contribute a large fraction of the total radiated
power, and sustain the formation of energetic kiloparsec scale lobes. While
observational properties of jets are widely differentiated, they are present in
high and l... | {
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"do... | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
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"G. B. Taylor",
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9a4fcf488ba6b8c32e9d1ae15954be0da2ba7486 | subsection | 2 | 19 | INTRODUCTION | Thanks to its proximity
and brightness, Mrk 501 is an ideal laboratory for experiments using these
advanced VLBI techniques: it is at z = 0.034 (1 mas = 0.67 pc, using H_0 =
70 km s^{-1} Mpc^{-1}); the total flux density at 5 GHz is S_5 =
1.4 Jy; the Schwarzschild radius for its central black hole is estimated
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07b79e7ebec32656b3c8b804647c9b732da1ec34 | subsection | 3 | 19 | High Sensitivity Array observations | We observed Mrk 501 with the HSA at 1.4 GHz on 26 Nov 2004. The HSA is
obtained by combining in the same array the 10 VLBA antennas and other
sensitive elements, i.e. the Green Bank Telescope (GBT, 100 m.), the phased VLA
(27 \times 25 m.), Arecibo (300 m.), and Effelsberg (100 m.). Even without
Arecibo, whose declinat... | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
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3cb7d35da1ee138a924e71c1b75da91059b59bdd | subsection | 4 | 19 | Global mm-VLBI observations | Millimeter VLBI permits a much higher angular resolution than ground or space
based VLBI at centimeter wavelengths. Moreover, it offers the possibility to
study emission regions which appear self-absorbed at longer wavelengths, with
important consequences for our understanding of the physical processes in AGNs
in the v... | {
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0983750a0659dc74ab064e97d6a0f967e0011f16 | subsection | 5 | 19 | The kpc scale structure | On kiloparsec scales, Mrk 501 is core dominated with a two sided extended
structure visible as well, extending in PA \sim 45^\circ for more than
30 on both sides of the core , , . It is
straightforward to identify this structure with the symmetric extended emission
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f8a223e7b58bf8c5946a287efa99be9c16ac5a0c | subsection | 6 | 19 | The extended jet | We obtain a detailed look at the jet of Mrk 501 from the deep VLBI observations
with the HSA. We show in Fig. REF a tapered image, where baselines
longer than 18 M\lambda have been significantly down-weighted to increase the
signal to noise ratio of the low-surface brightness emission. We achieve a
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few hundreds | [
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"G. B. Taylor",
"M. A. Perez-Torres",
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2f410ae1b407348f67484bb95d69df50de3f719a | subsection | 7 | 19 | The extended jet | A boxcar filter (50 mas) has been applied to smooth the data atr>50 mas.]We derived brightness profiles across the jet using the AIPS task
SLICE on the tapered HSA image for the extended jet, obtaining one
slice every 5 mas in PA=-56^\circ . Using the AIPS task SLFIT, we fitted
single Gaussian components to each profil... | {
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} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
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"G. B. Taylor",
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] | 2,008 | en | Physics | [
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b111c500ca6d5472d0b38f9ac4a35862ba6f1c49 | subsection | 8 | 19 | The core and inner jet structure | In Fig. REF , we show our Global mm-VLBI Array image of Mrk 501 at a
resolution of 110 \mu as \times \, 40 \, \mu as (beam FWHM, PA
-8^\circ ). Mrk 501 is clearly detected at 3 mm and it is dominated by a
compact, prominent component, \sim 45 mJy beam^{-1} peak brightness. The
visibility data suggest that there is a fa... | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
"M. Giroletti",
"G. Giovannini",
"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
"M. Chiaberge",
"P. G. Edwards"
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2c8bc62f48b76c1237dc16dcd90be24246b8314f | subsection | 9 | 19 | The core and inner jet structure | We then use our deconvolved size of
this component to give an upper limit to the dimension of the jet base, and a
lower limit to its brightness temperature. At z=0.034, 1 mas = 0.67 pc,
therefore the deconvolved angular size of the GMVA core corresponds to 0.021
\times 0.032 pc. The black hole mass for Mrk 501 is estim... | {
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} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
"M. Giroletti",
"G. Giovannini",
"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
"M. Chiaberge",
"P. G. Edwards"
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e8bf6c6caff97fa2b9d74fa3025712ddd685c39f | subsection | 10 | 19 | The core and inner jet structure | This implies that the turnover
frequency at \sim 8 GHz is related to the whole structure and not to the
86 GHz core, whose self-absorption peak is probably located at higher
frequency.We also plot in Fig. REF (dashed line) the difference between the
total single dish flux density and the VLBI core one. Apart from some
... | {
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"end... | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
"M. Giroletti",
"G. Giovannini",
"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
"M. Chiaberge",
"P. G. Edwards"
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4045d7ce60b9075948dc7013fe2f668dde52f078 | subsection | 11 | 19 | Polarization | In polarized intensity, previous VLBI observations of Mrk 501 have revealed
flux densities of a few milliJansky, i.e., a few percent of the total intensity
. Our new HSA observations confirm the presence of a significant
fraction of polarized flux and reveal interesting details (see
Figs. REF and REF ). The total flux ... | {
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few hundreds | [
"M. Giroletti",
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"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
"M. Chiaberge",
"P. G. Edwards"
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ff5bc223fa8d7d8fea719b85891554fa3b692e05 | subsection | 12 | 19 | DISCUSSION | In §, we have presented our main new results about the core
and jet of Mrk 501. We now discuss their relevance for our understanding of the
physics of this source and of AGNs and jets in general. | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
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"G. B. Taylor",
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a5d10f4a68eb406b1885e548e17fefe8d8b5d412 | subsection | 13 | 19 | The inner core: radio core spectrum and GMVA structure | The nuclear region of Mrk 501 consists of (1) an unresolved component: the
radio `core', point-like at our resolution (deconvolved size smaller than \sim 30 \times 20 \, \mu as or 0.020 \times 0.014 pc or 200 \times 140 R_S), and
(2) a faint resolved jet-like structure with a large opening angle, similar
(taking into a... | {
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"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
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295784d247e15027f31b7f7dc66000a55aec15d8 | subsection | 14 | 19 | Jet structure and polarization | Limb brightening in the jet of Mrk 501 seems to be present on scales as small
as 0.1 mas, but also after the two main bends at \sim 2 and \sim 20 mas,
where the jet has significantly expanded transversely. Under a given viewing
angle, different Doppler factors can arise from different velocities;
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few hundreds | [
"M. Giroletti",
"G. Giovannini",
"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
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652d1e0faf16ab1ff92a32cf6d74fc6502f4d4e3 | subsection | 15 | 19 | Jet structure and polarization | Because of different frequency and resolution, a
comparison of the datasets is not obvious; one can assume that the difference
in the polarization vector orientation is mainly due to Faraday Rotation or
that at 1.4 GHz the dominant polarized flux is from the jet inner spine, and
this polarized flux has vectors oriented... | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
"M. Giroletti",
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"G. B. Taylor",
"M. A. Perez-Torres",
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869eb1b96d0354be23a63c6ca4c87c97278908a2 | subsection | 16 | 19 | Jet velocity and orientation | Our results show that the jet in Mrk 501 is characterized by different
properties on the various scales from a few hundreds to several millions
Schwarzschild radii. The jet orientation and velocity, and the ratio between
spine and shear contributions must significantly change over these scales. It
is therefore impossib... | {
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few hundreds | [
"M. Giroletti",
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"W. D. Cotton",
"G. B. Taylor",
"M. A. Perez-Torres",
"M. Chiaberge",
"P. G. Edwards"
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a686d84046f828b77425959ed96db2477b567b67 | subsection | 17 | 19 | Jet velocity and orientation | Only
in the case of the smallest viewing angle (i.e. \theta = 5^\circ ) the jet
velocity falls off rapidly after the main jet bend; in the extended part of the
jet, narrow viewing angles are therefore not acceptable. However, it is
possible that the jet is more closely aligned in its inner part and then it
becomes orie... | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
few hundreds | [
"M. Giroletti",
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"G. B. Taylor",
"M. A. Perez-Torres",
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51e00ffd536860b8cb45089ea3b9a9989ea00e94 | subsection | 18 | 19 | CONCLUSIONS | We have successfully explored new regions in the remarkable jet of
Mrk 501. Thanks to the great sensitivity of the HSA, we reveal that the VLBI
jet is one-sided (and therefore in the relativistic regime) out to at least 500
parsecs from the core. The polarization vectors are clearly aligned with the
jet spine, suggesti... | {
"cite_spans": []
} | 10.1051/0004-6361:200809784 | 0807.1786 | The jet of Markarian 501 from millions of Schwarzschild radii down to a
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"G. B. Taylor",
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cb12bdea86b1f21b009e5d87007736e253177269 | abstract | 0 | 23 | Abstract | Double peaked broad emission lines in active galactic nuclei are generally
considered to be formed in an accretion disc. In this paper, we compute the
profiles of reprocessing emission lines from a relativistic, warped accretion
disc around a black hole in order to explore the possibility that certain
asymmetries in th... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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b1a62ca183a6e6707de6c32ce2a68d4b842c0d7f | subsection | 1 | 23 | Introduction | A small fraction of active galactic nuclei (AGN) show double-peaked
broad emission line profiles , , , . The
possibility has been considered for a long time that at least some
of these lines arise directly from the accretion discs assumed to
feed the central supermassive black holes. The H\alpha profile
observed in the... | {
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"end": 104,
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"raw": "Eracleous M., Halpern J. P., 1994, ApJS, 90, 1",
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"end": ... | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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