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Angular Momentum Induced In The Fermionic Vacuum On A Rotationally-Symmetric Noncompact Riemann Surface: The influence of spatial geometry on the vacuum polarization in 2+1-dimensional spinor electrodynamics is investigated. The vacuum angular momentum induced by an external static magnetic field is found to depend on global geometric surface characteristics connected with curvature. The relevance of the results obtained for the fermion number fractionization is discussed.
hep-th
Bifurcation and pattern changing with two real scalar fields: This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios between the various domain wall tensions can be reduced to 4 if the model has a superpotential. We then study specific one-parameter families of models and compute the wall tensions associated with both BPS and non-BPS sectors. We show how bifurcation can be associated to modification of the patterns of domain wall networks and illustrate this with some examples which may be relevant to describe realistic situations of current interest in high energy physics. In particular, we discuss a simple solution to the cosmological domain wall problem.
hep-th
Moduli Spaces for D-branes at the Tip of a Cone: For physicists: We show that the quiver gauge theory derived from a Calabi-Yau cone via an exceptional collection of line bundles on the base has the original cone as a component of its classical moduli space. For mathematicians: We use data from the derived category of sheaves on a Fano surface to construct a quiver, and show that its moduli space of representations has a component which is isomorphic to the anticanonical cone over the surface.
hep-th
Supersymmetric Intersecting Branes in Time-dependent Backgrounds: We construct a family of supersymmetric solutions in time-dependent backgrounds in supergravity theories. One class of the solutions are intersecting brane solutions and another class are brane solutions in pp-wave backgrounds, and their intersection rules are also given. The relation to existing literature is also discussed. An example of D1-D5 with linear null dilaton together with its possible dual theory is briefly discussed.
hep-th
Vulcanized Vortex: We investigate vortex configurations with the "vulcanization" term inspired by the renormalization of $\phi_\star^4$ theory in the canonical $\theta$-deformed noncommutativity. We focus on the classical limit of the theory described by a single parameter which is the ratio of the vulcanization and the noncommutativity parameters. We perform numerical calculations and find that nontopological vortex solutions exist as well as Q-ball type solutions, but topological vortex solutions are not admitted.
hep-th
Bootstrapping the String KLT Kernel: We show that a generalized version of the 4-point string theory KLT double-copy map is the most general solution to the minimal-rank double-copy bootstrap in effective field theory. This follows from significant restrictions of the 4-point map resulting from the 6-point bootstrap analysis. The generalized 4-point double-copy map is defined by a function with only two parameters times a simple function that is symmetric in $s,t,u$. The two parameters can be interpreted as independent choices of $\alpha'$, one for each of the two sets of amplitudes double-copied with the map. Specifically, each of those two sets of amplitudes must obey either the string monodromy relations or the field theory KK & BCJ relations; there are no other options. We propose a closed form of the new double-copy map that interpolates between the original KLT string double-copy and the open & closed string period integrals. The construction clarifies the "single-valued projection" property of the Riemann zeta-function values for the 4-point string theory double copy.
hep-th
Generating Vector Boson Masses: If the Higgs particle is never found, one will need an alternative theory for vector boson masses. I propose such a theory involving an antisymmetric tensor potential coupled to a gauge field.
hep-th
T-duality and U-duality in toroidally-compactified strings: We address the issue of T-duality and U-duality symmetries in the toroidally-compactified type IIA string. It is customary to take as a starting point the dimensionally-reduced maximal supergravity theories, with certain field strengths dualised such that the classical theory exhibits a global $E_{n(n)}$ symmetry, where n=11-D in D dimensions. A discrete subgroup then becomes the conjectured U-duality group. In dimensions D\le 6, these necessary dualisations include NS-NS fields, whose potentials, rather than merely their field strengths, appear explicitly in the couplings to the string worldsheet. Thus the usually-stated U-duality symmetries act non-locally on the fundamental fields of perturbative string theory. At least at the perturbative level, it seems to be more appropriate to consider the symmetries of the versions of the lower-dimensional supergravities in which no dualisations of NS-NS fields are required, although dualisations of the R-R fields are permissible since these couple to the string through their field strengths. Taking this viewpoint, the usual T-duality groups survive unscathed, as one would hope since T-duality is a perturbative symmetry, but the U-duality groups are modified in D\le 6.
hep-th
A Note on a Generalized AHM Model with Analytical Vortex Solutions: We study topological vortex solutions in a generalized Abelian Higgs model with non-polynomial dielectric and potential functions. These quantities are chosen by requiring integrability of the self-dual limit of the theory for all values of the magnetic flux. All the vortex profiles are described by exact analytical expressions that solve the self-dual vortex equations. There is only a symmetry-breaking superconducting phase and the model sustains regular phenomenology.
hep-th
Generalized heat kernel coefficients: Following Osipov and Hiller, a generalized heat kernel expansion is considered for the effective action of bosonic operators. In this generalization, the standard heat kernel expansion, which counts inverse powers of a c-number mass parameter, is extended by allowing the mass to be a matrix in flavor space. We show that the generalized heat kernel coefficients can be related to the standard ones in a simple way. This holds with or without trace and integration over spacetime, to all orders and for general flavor spaces. Gauge invariance is manifest.
hep-th
Entanglement of Purification and Projective Measurement in CFT: We investigate entanglement of purification in conformal field theory. By using Reeh-Schlieder theorem, we construct a set of the purification states for $\rho_{AB}$, where $\rho_{AB}$ is reduced density matrix for subregion $AB$ of a global state $\rho$. The set can be approximated by acting all the unitary observables,located in the complement of subregion $AB$, on the global state $\rho$, as long as the global state $\rho$ is \text{cyclic} for every local algebra, e.g., the vacuum state. Combining with the gravity explanation of unitary operations in the context of the so-called surface/state correspondence, we prove the holographic EoP formula. We also explore the projective measurement with the conformal basis in conformal field theory and its relation to the minimization procedure of EoP. Interestingly, though the projective measurement is not a unitary operator, the difference in some limits between holographic EoP and the entanglement entropy after a suitable projective measurement is a constant $\frac{c}{3}\log 2$ up to some contributions from boundary. This suggests the states after projective measurements may approximately be taken as the purification state corresponding to the minimal value of the procedure.
hep-th
Smooth non-extremal D1-D5-P solutions as charged gravitational instantons: We present an alternative and more direct construction of the non-supersymmetric D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. We show that these solutions --- with all three charges and both rotations turned on --- can be viewed as a charged version of the Myers-Perry instanton. We present an inverse scattering construction of the Myers-Perry instanton metric in Euclidean five-dimensional gravity. The angular momentum bounds in this construction turn out to be precisely the ones necessary for the smooth microstate geometries. We add charges on the Myers-Perry instanton using appropriate SO(4,4) hidden symmetry transformations. The full construction can be viewed as an extension and simplification of a previous work by Katsimpouri, Kleinschmidt and Virmani.
hep-th
Ambiguity in mana and magic definition and knot states: We study the Mana and Magic for quantum states. They have a standard definition through the Clifford group, which is finite and thus classically computable. We introduce a modified Mana and Magic, which keep their main property of classical computability, while making other states classically computable. We also apply these new definitions to the studies of knot states of 2-strand knots.
hep-th
Quantum corrected gravitational potential beyond monopole-monopole interactions: We investigate spin- and velocity-dependent contributions to the gravitational inter-particle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections. Restricting ourselves to corrections up to the level of the graviton propagator, we compute, in terms of general form factors, the non-relativistic gravitational potential associated with the scattering of spin-0 and -1/2 particles. We discuss comparative aspects concerning different types of scattered particles and we also establish some comparisons with the case of electromagnetic potentials. Moreover, we apply our results to explicit examples of form factors based on non-perturbative approaches for quantum gravity. Finally, the cancellation of Newtonian singularity is analysed in the presence of terms beyond the monopole-monopole sector.
hep-th
Affine Symmetries for ABJM Partition Function and its Generalization: Partially motivated by the fact that the grand partition function of the ABJM theory or its generalization is expressed by a spectral operator enjoying symmetries of the Weyl group, it was found that the grand partition function satisfies the q-Painleve equation, which is constructed from the affine Weyl group. In this paper we clarify the affine symmetries of the grand partition function. With the affine symmetries, we find that the grand partition function extends naturally outside the fundamental domain of duality cascades and once the Painleve equation holds in the fundamental domain, so does it outside.
hep-th
Self--dual Lorentzian wormholes in n--dimensional Einstein gravity: A family of spherically symmetric, static and self--dual Lorentzian wormholes is obtained in n--dimensional Einstein gravity. This class of solutions includes the n--dimensional versions of the Schwarzschild black hole and the spatial--Schwarzschild traversable wormhole. Using isotropic coordinates we study the geometrical structure of the solution, and delineate the domains of the free parameters for which wormhole, naked singular geometries and the Schwarzschild black hole are obtained. It is shown that, in the lower dimensional Einstein gravity without cosmological constant, we can not have self--dual Lorentzian wormholes.
hep-th
The Canonical Symmetry and Hamiltonian Formalism. I. Conservation Laws: The properties of the canonical symmetry of the nonlinear Schr\"odinger equation are investigated. The densities of the local conservation laws for this system are shown to change under the action of the canonical symmetry by total space derivatives.
hep-th
A Web of 2d Dualities: ${\bf Z}_2$ Gauge Fields and Arf Invariants: We describe a web of well-known dualities connecting quantum field theories in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global symmetries and includes a number of perennial favourites such as the Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac fermion, and T-duality. There are also less-loved examples, such as non-modular invariant $c=1$ CFTs that depend on a background spin structure.
hep-th
Quantization Rules for Dynamical Systems: We discuss a manifestly covariant way of arriving at the quantization rules based on causality, with no reference to Poisson or Peierls brackets of any kind.
hep-th
The three-loop Adler $D$-function for ${\cal N}=1$ SQCD with various renormalization prescriptions: The three-loop Adler $D$-function for ${\cal N}=1$ SQCD in the $\overline{\mbox{DR}}$ scheme is calculated. It appears that the result does not satisfy NSVZ-like equation which relates the $D$-function to the anomalous dimension of the matter superfields. However this NSVZ-like equation can be restored by a special tuning of the renormalization scheme. Also we demonstrate that the $D$-function defined in terms of the bare coupling does not satisfy the NSVZ-like equation in the case of using the regularization by dimensional reduction. The scheme-dependence of the $D$-function written in the form of the $\beta$-expansion is briefly discussed.
hep-th
Breakdown of Cluster Decomposition in Instanton Calculations of the Gluino Condensate: A longstanding puzzle concerns the calculation of the gluino condensate <{tr\lambda^2\over 16\pi^2}> = c\Lambda^3 in N=1 supersymmetric SU(N) gauge theory: so-called weak-coupling instanton (WCI) calculations give c=1, whereas strong-coupling instanton (SCI) calculations give, instead, c=2[(N-1)!(3N-1)]^{-1/N}. By examining correlators of this condensate in arbitrary multi-instanton sectors, we cast serious doubt on the SCI calculation of <{tr\lambda^2\over 16\pi^2}> by showing that an essential step --- namely cluster decomposition --- is invalid. We also show that the addition of a so-called Kovner-Shifman vacuum (in which <{tr\lambda^2\over 16\pi^2}> = 0) cannot straightforwardly resolve this mismatch.
hep-th
Causality and classical dispersion relations: We explore the consequences of relativistic causality and covariant stability for short-wavelength dispersion relations in classical systems. For excitations described by a finite number of partial differential equations, as is the case in relativistic hydrodynamics, we give causality and covariant stability constraints on the excitation's frequency at large momenta.
hep-th
Israel--Wilson--Perjés Solutions in Heterotic String Theory: We present a simple algorithm to obtain solutions that generalize the Israel--Wilson--Perj\'es class for the low-energy limit of heterotic string theory toroidally compactified from D=d+3 to three dimensions. A remarkable map existing between the Einstein--Maxwell (EM) theory and the theory under consideration allows us to solve directly the equations of motion making use of the matrix Ernst potentials connected with the coset matrix of heterotic string theory. For the particular case d=1 (if we put n=6, the resulting theory can be considered as the bosonic part of the action of D=4, N=4 supergravity) we obtain explicitly a dyonic solution in terms of one real 2\times 2--matrix harmonic function and 2n real constants (n being the number of Abelian vector fields). By studying the asymptotic behaviour of the field configurations we define the charges of the system. They satisfy the Bogomol'nyi--Prasad--Sommmerfeld (BPS) bound.
hep-th
Correlators of Vertex Operators for Circular Strings with Winding Numbers in AdS5xS5: We compute semiclassically the two-point correlator of the marginal vertex operators describing the rigid circular spinning string state with one large spin and one windining number in AdS_5 and three large spins and three winding numbers in S^5. The marginality condition and the conformal invariant expression for the two-point correlator obtained by using an appropriate vertex operator are shown to be associated with the diagonal and off-diagonal Virasoro constraints respectively. We evaluate semiclassically the three-point correlator of two heavy circular string vertex operators and one zero-momentum dilaton vertex operator and discuss its relation with the derivative of the dimension of the heavy circular string state with respect to the string tension.
hep-th
Canonical invariance of spatially covariant scalar-tensor theory: We investigate invariant canonical transformations of a spatially covariant scalar-tensor theory of gravity, called the XG theory, by which the action or the Hamiltonian and the primary constraints keep their forms invariant. We derive the Hamiltonian in a non perturbative manner and complete the Hamiltonian analysis for all regions of the theory. We confirm that the theory has at most 3 degrees of freedom in all regions of the theory as long as the theory has the symmetry under the spatial diffeormorphism. Then, we derive the invariant canonical transformation by using the infinitesimal transformation. The invariant metric transformation of the XG theory contains a vector product as well as the disformal transformation. The vector product and the disformal factor can depend on the higher order derivative terms of the scalar field and the metric. In addition, we discover the invariant canonical transformation which transforms the momentum of the metric. Using the invariant transformation, we study the relation between the Horndeski theory and the GLPV theory, and find that we can not obtain the arbitrary GLPV theory from the Horndeski theory through the invariant canonical transformation we have found.
hep-th
$T\bar{T}$ deformed partition functions: We demonstrate the presence of modular properties in partition functions of $T\bar{T}$ deformed conformal field theories. These properties are verified explicitly for the deformed free boson. The modular features facilitate a derivation of the asymptotic density of states in these theories, which turns out to interpolate between Cardy and Hagedorn behaviours. We also point out a sub-sector of the spectrum that remains undeformed under the $T\bar{T}$ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.
hep-th
Statistical mechanics for dilatations in N=4 super Yang--Mills theory: Matrix model describing the anomalous dimensions of composite operators in $\mathcal{N}=4$ super Yang--Mills theory up to one-loop level is considered at finite temperature. We compute the thermal effective action for this model, which we define as the log of the partition function restricted to the states of given fixed length and spin. The result is obtained in the limits of high and low temperature.
hep-th
A Comment on the Odd Flows for the Supersymmetric KdV equation: In a recent paper Dargis and Mathieu introduced integrodifferential odd flows for the supersymmetric KdV equation. These flows are obtained from the nonlocal conservation laws associated with the fourth root of its Lax operator. In this note I show that only half of these flows are of the standard Lax form, while the remaining half provide us with hamiltonians for an SKdV-type reduction of a new supersymmetric hierarchy. This new hierarchy is shown to be closely related to the Jacobian supersymmetric KP-hierarchy of Mulase and Rabin. A detailed study of the algebra of additional symmetries of this new hierarchy reveals that it is isomorphic to the super-W_{1+\infty} algebra, thus making it a candidate for a possible interrelationship between superintegrability and two-dimensional supergravity.
hep-th
BRST invariant $CP^{1}$ model through improved Dirac quantization: The Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the $CP^1$ model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the $CP^1$ model. Exploiting the Hopf bundle, we also show that the $CP^1$ model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.
hep-th
Fluctuation and Dissipation from a Deformed String/Gauge Duality Model: Using a Lorentz invariant deformed string/gauge duality model at finite temperature we calculate the thermal fluctuation and the corresponding linear response, verifying the fluctuation-dissipation theorem. The deformed AdS$_5$ is constructed by the insertion of an exponential factor $\exp(k/r^2)$ in the metric. We also compute the string energy and the mean square displacement in order to investigate the ballistic and diffusive regimes. Furthermore we have studied the dissipation and the linear response in the zero temperature scenario.
hep-th
Supergravity couplings: a geometric formulation: This report provides a pedagogical introduction to the description of the general Poincare supergravity/matter/Yang-Mills couplings using methods of Kahler superspace geometry. At a more advanced level this approach is generalized to include tensor field and Chern-Simons couplings in supersymmetry and supergravity, relevant in the context of weakly and strongly coupled string theories.
hep-th
Discrete Theta Angles, Symmetries and Anomalies: Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and 't Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d QCD with $SU(N),SU(N)/\mathbb{Z}_k$ or $SO(N)$ gauge groups as well as various 3d and 2d gauge theories.
hep-th
Proof of a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity: A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered.
hep-th
On Lie point symmetry of classical Wess-Zumino-Witten model: We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical Wess-Zumino-Witten model. We also consider variations of this model. Our analysis gives the generators of the corresponding Lie point symmetries. The Lie symmetry corresponding to Kepler's third law is obtained in two related examples.
hep-th
Complementarity in Wormhole Chromodynamics: The electric charge of a wormhole mouth and the magnetic flux ``linked'' by the wormhole are non-commuting observables, and so cannot be simultaneously diagonalized. We use this observation to resolve some puzzles in wormhole electrodynamics and chromodynamics. Specifically, we analyze the color electric field that results when a colored object traverses a wormhole, and we discuss the measurement of the wormhole charge and flux using Aharonov-Bohm interference effects. We suggest that wormhole mouths may obey conventional quantum statistics, contrary to a recent proposal by Strominger.
hep-th
Extremal Black Brane Attractors on The Elliptic Curve: Reconsidering the analysis of the moduli space of N=2 eight dimensional supergravity coupled to seven scalars, we propose a new scalar manifold factorization given by \frac{\textsc {SO(2,2)}}{{\textsc{SO(2)}}\times {\textsc{SO(2)}}}\times \frac{\textsc{SO(2,1)}}{\textsc{SO(2)}}\times \textsc {SO(1,1)}. This factorization is supported by the appearance of three solutions of Type IIA extremal black p-branes (p=0,1,2) with AdS_{p+2}\times S^{6-p} near-horizon geometries in eight dimensions. We analyze the corresponding attractor mechanism. In particular, we give an interplay between the scalar manifold factors and the extremal black p-brane charges. Then we show that the dilaton can be stabilized by the dyonic black 2-brane charges.
hep-th
On the renormalisation group for the boundary Truncated Conformal Space Approach: In this paper we continue the study of the truncated conformal space approach to perturbed boundary conformal field theories. This approach to perturbation theory suffers from a renormalisation of the coupling constant and a multiplicative renormalisation of the Hamiltonian. We show how these two effects can be predicted by both physical and mathematical arguments and prove that they are correct to leading order for all states in the TCSA system. We check these results using the TCSA applied to the tri-critical Ising model and the Yang-Lee model. We also study the TCSA of an irrelevant (non-renormalisable) perturbation and find that, while the convergence of the coupling constant and energy scales are problematic, the renormalised and rescaled spectrum remain a very good fit to the exact result, and we find a numerical relationship between the IR and UV couplings describing a particular flow. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points.
hep-th
Comments on Quivers and Fractons: We discuss certain structural analogies between supersymmetric quiver gauge theories and lattice models leading to fracton phases of matter. In particular, classes of quiver models can be viewed as lattice models having sub-system symmetries, dimensions of moduli spaces growing linearly with the size of the lattice, and having excitations with limited mobility (with "excitations" and "mobility" properly defined).
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Basic zeta functions and some applications in physics: It is the aim of these lectures to introduce some basic zeta functions and their uses in the areas of the Casimir effect and Bose-Einstein condensation. A brief introduction into these areas is given in the respective sections. We will consider exclusively spectral zeta functions, that is zeta functions arising from the eigenvalue spectrum of suitable differential operators. There is a set of technical tools that are at the very heart of understanding analytical properties of essentially every spectral zeta function. Those tools are introduced using the well-studied examples of the Hurwitz, Epstein and Barnes zeta function. It is explained how these different examples of zeta functions can all be thought of as being generated by the same mechanism, namely they all result from eigenvalues of suitable (partial) differential operators. It is this relation with partial differential operators that provides the motivation for analyzing the zeta functions considered in these lectures. Motivations come for example from the questions "Can one hear the shape of a drum?" and "What does the Casimir effect know about a boundary?". Finally "What does a Bose gas know about its container?"
hep-th
A Relativistic Quaternionic Wave Equation: We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved quantity which looks like helicity. The principle of superposition is retained in a slightly altered manner. External potentials can be introduced in a way that allows for gauge invariance. There are some results for scattering theory and for two-particle wavefunctions as well as the beginnings of second quantization. However, we are unable to find a suitable Lagrangian or an energy-momentum tensor.
hep-th
Exact One-Point Function of N=1 super-Liouville Theory with Boundary: In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space-time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with discrete (NS) boundary conditions and for the theory with explicit boundary actions which preserves super conformal symmetries. We provide various consistency checks. We also show that these one-point functions can be related to a generalized Cardy conditions along with corresponding modular $S$-matrices. Using this result, we conjecture the dependence of the boundary two-point functions of the (NS) boundary operators on the boundary parameter.
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Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities: The chiral superstring measure constructed in the earlier papers of this series for general gravitino slices is examined in detail for slices supported at two points x_\alpha. In this case, the invariance of the measure under infinitesimal changes of gravitino slices established previously is strengthened to its most powerful form: the measure is shown, point by point on moduli space, to be locally and globally independent from the points x_\alpha, as well as from the superghost insertion points p_a, q_\alpha introduced earlier as computational devices. In particular, the measure is completely unambiguous. The limit x_\alpha = q_\alpha is then well defined. It is of special interest, since it elucidates some subtle issues in the construction of the picture-changing operator Y(z) central to the BRST formalism. The formula for the chiral superstring measure in this limit is derived explicitly.
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Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras: We study realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary highest-weight representations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G_2, with the central charges c_8=26/5 and c_7=5, respectively. Furthermore, we show that the general coset Ans"atze for the N=8 and N=7 algebras naturally lead to the coset spaces SO(8)xU(1)/SO(7) and SO(7)xU(1)/G_2, respectively, as the additional consistent solutions for certain values of the central charge. The coset space SO(8)/SO(7) is the seven-sphere S^7, whereas the space SO(7)/G_2 represents the seven-sphere with torsion, S^7_T. The division algebra of octonions and the associated triality properties of SO(8) play an essential role in all these realizations. We also comment on some possible applications of our results to string theory.
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The Search for Zoo-Perparticles: This paper reviews the covariant formalism of N=1, D=10 classical superparticle models. It discusses the local invariances of a number of superparticle actions and highlights the problem of finding a covariant quantization scenario. Covariant quantization has proved problematic, but it has motivated in seeking alternative approaches that avoids those found in earlier models. It also shows new covariant superparticle theories formulated in extended spaces that preserve certain canonical form in phase-space, and easy to quantize by using the Batalin-Vilkovisky procedure, as the gauge algebra of their constraints only closes on-shell. The mechanics actions describe particles moving in a superspace consisting of the usual $N=1$ superspace, together with an extra spinor or vector coordinate. A light-cone analysis shows that all these new superparticle models reproduce the physical spectrum of the N=1 super-Yang-Mills theory.
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Exact Inner Metric and Microscopic State of AdS$_3$-Schwarzschld BHs: Through full solvability of 2+1 dimensional general relativity we derive out exact dynamic inner metric of collapsing stars with inhomogeneous initial mass distribution but joining with outside Anti-deSitt-Schwarzschild black holes smoothly. We prove analytically by standard quantum mechanics that the log-number of such solutions, or microscopic states of the system is proportional to the perimeter of the outside black holes. Key formulas for generalizing to 3+1D Schwarzschild black holes are also presented. Our result provides a bulk space viewpoint to questions on what the microscopic degrees of freedom are and who their carriers are in various holographic and/or asymptotic symmetry methods to black hole entropies. It may also shed light for singularity theorem and cosmic censorship related researches.
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Torsional Regularization of Self-Energy and Bare Mass of Electron: In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum. In the Einstein--Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum. Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums. In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics. We show that this procedure eliminates the ultraviolet divergence. We also show that torsion gives a photon a small nonzero mass, which regularizes the infrared divergence. In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$, $90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively. These values constitute about $85\%$ of the observed, re-normalized masses.
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Astrophysical Violations of the Kerr Bound as a Possible Signature of String Theory: In 4D general relativity, the angular momentum of a black hole is limited by the Kerr bound. We suggest that in string theory, this bound can be breached and compact black-hole-like objects can spin faster. Near such "superspinars," the efficiency of energy transfer from the accreting matter to radiation can reach 100%, compared to the maximum efficiency of 42% of the extremal Kerr (or 6% of the Schwarzschild) black hole. Finding such superspinning objects as active galactic nuclei, GBHCs, or sources of gamma ray bursts, could be viewed as experimental support for string theory.
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Chaos around Holographic Regge Trajectories: Using methods of Hamiltonian dynamical systems, we show analytically that a dynamical system connected to the classical spinning string solution holographically dual to the principal Regge trajectory is non-integrable. The Regge trajectories themselves form an integrable island in the total phase space of the dynamical system. Our argument applies to any gravity background dual to confining field theories and we verify it explicitly in various supergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and the AdS soliton. Having established non-integrability for this general class of supergravity backgrounds, we show explicitly by direct computation of the Poincare sections and the largest Lyapunov exponent, that such strings have chaotic motion.
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Hierarchy problem and the cosmological constant in a five-dimensional Brans-Dicke brane world model: We discuss a new solution, admitting the existence of dS_{4} branes, in five-dimensional Brans-Dicke theory. It is shown that, due to a special form of a bulk scalar field potential, for certain values of the model parameters the effective cosmological constant can be made small on the brane, where the hierarchy problem of gravitational interaction is solved. We also discuss new stabilization mechanism which is based on the use of auxiliary fields.
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Hawking temperature from tunnelling formalism: It has recently been suggested that the attempt to understand Hawking radiation as tunnelling across black hole horizons produces a Hawking temperature double the standard value. It is explained here how one can obtain the standard value in the same tunnelling approach.
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2d Index and Surface operators: In this paper we compute the superconformal index of 2d (2,2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong. In the later half of the paper, we study half-BPS surface operators in N=2 superconformal gauge theories. They are engineered by coupling the 2d (2,2) supersymmetric gauge theory living on the support of the surface operator to the 4d N=2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.
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New Multicritical Random Matrix Ensembles: In this paper we construct a class of random matrix ensembles labelled by a real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves like $|x|^\alpha$. The eigenvalue spacing near zero scales like $1/N^{1/(1+\alpha)}$ and thus these ensembles are representatives of a {\em continous} series of new universality classes. We study these ensembles both in the bulk and on the scale of eigenvalue spacing. In the former case we obtain formulas for the eigenvalue density, while in the latter case we obtain approximate expressions for the scaling functions in the microscopic limit using a very simple approximate method based on the location of zeroes of orthogonal polynomials.
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Stability of $AdS_p x S^n x S^{q-n}$ Compactifications: We examine the stability of ${\rm AdS}_p \times {\rm S}^n \times {\rm S}^{q-n}$. The initial data constructed by De Wolfe et al \cite{Gary} has been carefully analyised and we have confirmed that there is no lower bound for the total mass for $q< 9$. The effective action on ${\rm AdS}_p$ has been derived for dilatonic compactification of the system to describe the non-linear fluctuation of the background space-time. The stability is discussed applying the positive energy theorem to the effective theory on AdS, which again shows the stability for $q \geq 9$.
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Integrable XYZ Model with Staggered Anisotropy Parameter: We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.
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Local Fluid Dynamical Entropy from Gravity: Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.
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Basic hypergeometry of supersymmetric dualities: We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities.
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Symmetries and supersymmetries of the Dirac operators in curved spacetimes: It is shown that the main geometrical objects involved in all the symmetries or supersymmetries of the Dirac operators in curved manifolds of arbitrary dimensions are the Killing vectors and the Killing-Yano tensors of any ranks. The general theory of external symmetry transformations associated to the usual isometries is presented, pointing out that these leave the standard Dirac equation invariant providing the correct spin parts of the group generators. Furthermore, one analyzes the new type of symmetries generated by the covariantly constant Killing-Yano tensors that realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. In this way the Dirac operators are related among themselves through continuous transformations associated to specific discrete ones. It is shown that the groups of this continuous symmetry can be only U(1) or SU(2), as those of the (hyper-)Kahler spaces, but arising even in cases when the requirements for these special geometries are not fulfilled. To exemplify, the Euclidean Taub-NUT space with its Dirac-type operators is presented in much details, pointing out that there is an infinite-loop superalgebra playing the role of a closed dynamical algebraic structure. As a final topic, we go to consider the properties of the Dirac-type operators of the Minkowski spacetime.
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Topological Gravity as the Early Phase of Our Universe: Motivated by string dualities we propose topological gravity as the early phase of our universe. The topological nature of this phase naturally leads to the explanation of many of the puzzles of early universe cosmology. A concrete realization of this scenario using Witten's four dimensional topological gravity is considered. This model leads to the power spectrum of CMB fluctuations which is controlled by the conformal anomaly coefficients $a,c$. In particular the strength of the fluctuation is controlled by $1/a$ and its tilt by $c g^2$ where $g$ is the coupling constant of topological gravity. The positivity of $c$, a consequence of unitarity, leads automatically to an IR tilt for the power spectrum. In contrast with standard inflationary models, this scenario predicts $\mathcal{O}(1)$ non-Gaussianities for four- and higher-point correlators and the absence of tensor modes in the CMB fluctuations.
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The AdS Virasoro-Shapiro Amplitude: We present a constructive method to compute the AdS Virasoro-Shapiro amplitude, order by order in AdS curvature corrections. At kth order the answer takes the form of a genus zero world-sheet integral involving weight 3k single-valued multiple polylogarithms. The coefficients in our ansatz are fixed, order by order, by requiring: crossing symmetry; the correct supergravity limit; the correct structure of poles, determined by dispersive sum rules; and the dimensions of the first few Konishi-like operators, available from integrability. We explicitly construct the first two curvature corrections. Our final answer then reproduces all localisation results and all CFT data available from integrability, to this order, and produces a wealth of new CFT data for planar N=4 SYM at strong coupling.
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Enhanced D-Brane Categories from String Field Theory: We construct D-brane categories in B-type topological string theory as solutions to string field equations of motion. Using the formalism of superconnections, we show that these solutions form a variant of a construction of Bondal and Kapranov. This analysis is an elaboration on recent work of Lazaroiu. We also comment on the relation between string field theory and the derived category approach of Douglas, and Aspinwall and Lawrence. Non-holomorphic deformations make a somewhat unexpected appearance in this construction.
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Holographic entanglement density for spontaneous symmetry breaking: We investigate the properties of the holographic entanglement entropy of the systems in which the $U(1)$ or the translational symmetry is broken \textit{spontaneously}. For this purpose, we define the entanglement density of the strip-subsystems and examine both the first law of entanglement entropy (FLEE) and the area theorem. We classify the conditions that FLEE and/or the area theorem obey and show that such a classification may be useful for characterizing the systems. We also find universalities from both FLEE and the area theorem. In the spontaneous symmetry breaking case, FLEE is always obeyed regardless of the type of symmetry: $U(1)$ or translation. For the translational symmetry, the area theorem is always violated when the symmetry is weakly broken, independent of the symmetry breaking patterns (explicit or spontaneous). We also argue that the $\log$ contribution of the entanglement entropy from the Goldstone mode may not appear in the strongly coupled systems.
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A Description of Schwarzschild Black Holes in terms of Intersecting M-branes and antibranes: Intersecting M-branes are known to describe multi charged black holes. Using a configuration of such intersecting branes and antibranes, together with massless excitations living on them, we give a description of Schwarzschild black holes following Danielsson, Guijosa, and Kruczenski. We calculate the entropy of these black holes and find that it agrees, upto a numerical factor, with the entropy of the corresponding Schwarzschild black holes in supergravity approximation. We give an empirical interpretation of this factor.
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Fermionic Zero Mode and String Creation between D4-Branes at Angles: We study the creation of a fundamental string between D4-branes at angles in string theory. It is shown that $R(-1)^{F}$ part of the one-loop potential of open string changes its sign due to the change of fermionic zero-mode vacua when the branes cross each other. As a result the effective potential is independent of the angles when supersymmetry is partially unbroken, and leads to a consistent picture that a fundamental string is created in the process. We also discuss the s-rule in the configuration. The same result is obtained from the one-loop potential for the orthogonal D4-branes with non-zero field strength. The result is also confirmed from the tension obtained by deforming the Chern-Simons term on one D4-brane, which is induced by another tilted D4-brane.
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Supersymmetric K field theories and defect structures: We construct supersymmetric K field theories (i.e., theories with a non-standard kinetic term) in 1+1 and 2+1 dimensions such that the bosonic sector just consists of a nonstandard kinetic term plus a potential. Further, we study the possibility of topological defect formation in these supersymmetric models. Finally, we consider more general supersymmetric K field theories where, again, topological defects exist in some cases.
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Renormalized Holographic Subregion Complexity under Relevant Perturbations: We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS$_4$ and AdS$_5$ geometries under relevant perturbations. Using the holographic renormalization method developed in the gauge/gravity duality, we obtain counter terms which are invariant under coordinate choices. We explicitly define different forms of renormalized HEE and HSC, according to conformal dimensions of relevant operators in the $d=3$ and $d=4$ dual field theories. We use a general embedding for arbitrary entangling subregions and showed that any choice of the coordinate system gives the same form of the counter terms, since they are written in terms of curvature invariants and scalar fields on the boundaries. We show an explicit example of our general procedure. Intriguingly, we find that a divergent term of the HSC in the asymptotically AdS$_5$ geometry under relevant perturbations with operators of conformal dimensions in the range $0< \Delta < \frac{1}{2}\,\, {\rm and} \,\, \frac{7}{2}< \Delta < 4$ cannot be cancelled out by adding any coordinate invariant counter term. This implies that the HSCs in these ranges of the conformal dimensions are not renormalizable covariantly.
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Null Infinity as a Weakly Isolated Horizon: Null infinity (Scri) arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that Scri is a weakly isolated horizon (WIH), and then show that its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs is very different from that extracted at Scri. We show that these differences can be directly traced back to the fact that Scri is a WIH in the conformal completion rather than the physical space-time. In particular, the BMS group at Scri stems from the symmetry group of WIHs. We also introduce a unified procedure to arrive at fluxes and charges associated with the BMS symmetries at Scri and those associated with black hole (and cosmological) horizons. This procedure differs from those commonly used in the literature and its novel elements seem interesting in their own right. The fact that is there is a single mathematical framework underlying black hole (and cosmological) horizons and Scri paves the way to explore the relation between horizon dynamics in the strong field region and waveforms at infinity. It should also be useful in the analysis of black hole evaporation in quantum gravity.
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Entropy and Black Holes in the Very Early Universe: Model independent arguments following from the Covariant Entropy Principle imply that causal diamonds in the very early universe were entirely filled with a single equilibrated system with finite entropy. A universe where this condition persists forever has no localized excitations. Our own universe appears to be headed toward such a state. Within a few hundred times its current age it will approach a state where our local group of galaxies sit in empty de Sitter space. Eventually, the local group collapse into a black hole, which evaporates. Localized excitations in de Sitter space are low entropy constrained states of the vacuum ensemble. The origin of these constraints must be in the early universe: the apparent horizon must expand after some initial period, in a constrained state that is the origin of all localized excitations in the universe. We argue that in global FRW coordinates, this corresponds to slow roll inflation that ends in a dilute gas of tiny black holes, with mass determined by the inflationary scale. We then review arguments that these black holes can account for the Hot Big Bang, baryogenesis, a distinctive pattern of CMB fluctuations, and possibly primordial black hole dark matter consisting of larger black holes that survive until the matter dominated era. The more complicated question of whether these small black holes can evolve in a way that is consistent with all observational constraints requires computer simulations that have not yet been done.
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Higher-Derivative Chiral Superfield Actions Coupled to N=1 Supergravity: We construct N=1 supergravity extensions of scalar field theories with higher-derivative kinetic terms. Special attention is paid to the auxiliary fields, whose elimination leads not only to corrections to the kinetic terms, but to new expressions for the potential energy as well. For example, a potential energy can be generated even in the absence of a superpotential. Our formalism allows one to write a supergravity extension of any higher-derivative scalar field theory and, therefore, has applications to both particle physics and cosmological model building. As an illustration, we couple the higher-derivative DBI action describing a 3-brane in 6-dimensions to N=1 supergravity. This displays a number of new features-- including the fact that, in the regime where the higher-derivative kinetic terms become important, the potential tends to be everywhere negative.
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Exact g-function flows from the staircase model: Equations are found for exact g-functions corresponding to integrable bulk and boundary flows between successive unitary c<1 minimal conformal field theories in two dimensions, confirming and extending previous perturbative results. These equations are obtained via an embedding of the flows into a boundary version of Al. Zamolodchikov's staircase model.
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Asymptotic symmetries of QED and Weinberg's soft photon theorem: Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.
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Entanglement and mutual information in two-dimensional nonrelativistic field theories: We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.
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Domain Wall and de Sitter Solutions of Gauged Supergravity: BPS domain wall solutions of gauged supergravities are found, including those theories which have non-compact gauge groups. These include models that have both an unstable de Sitter solution and stable domain wall solutions.
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A double integral of dlog forms which is not polylogarithmic: Feynman integrals are central to all calculations in perturbative Quantum Field Theory. They often give rise to iterated integrals of dlog-forms with algebraic arguments, which in many cases can be evaluated in terms of multiple polylogarithms. This has led to certain folklore beliefs in the community stating that all such integrals evaluate to polylogarithms. Here we discuss a concrete example of a double iterated integral of two dlog-forms that evaluates to a period of a cusp form. The motivic versions of these integrals are shown to be algebraically independent from all multiple polylogarithms evaluated at algebraic arguments. From a mathematical perspective, we study a mixed elliptic Hodge structure arising from a simple geometric configuration in $\mathbb{P}^2$, consisting of a modular plane elliptic curve and a set of lines which meet it at torsion points, which may provide an interesting worked example from the point of view of periods, extensions of motives, and L-functions.
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Towards a string representation of infrared SU(2) Yang-Mills theory: We employ a heat kernel expansion to derive an effective action that describes four dimensional SU(2) Yang-Mills theory in the infrared limit. Our result supports the proposal that at large distances the theory is approximated by the dynamics of knotted string-like fluxtubes which appear as solitons in the effective theory.
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The classical dynamics of gauge theories in the deep infrared: Gauge and gravitational theories in asymptotically flat settings possess infinitely many conserved charges associated with large gauge transformations or diffeomorphisms that are nontrivial at infinity. To what extent do these charges constrain the scattering in these theories? It has been claimed in the literature that the constraints are trivial, due to a decoupling of hard and soft sectors for which the conserved charges constrain only the dynamics in the soft sector. We show that the argument for this decoupling fails due to the failure in infinite dimensions of a property of symplectic geometry which holds in finite dimensions. Specializing to electromagnetism coupled to a massless charged scalar field in four dimensional Minkowski spacetime, we show explicitly that the two sectors are always coupled using a perturbative classical computation of the scattering map. Specifically, while the two sectors are uncoupled at low orders, they are coupled at quartic order via the electromagnetic memory effect. This coupling cannot be removed by adjusting the definitions of the hard and soft sectors (which includes the classical analog of dressing the hard degrees of freedom). We conclude that the conserved charges yield nontrivial constraints on the scattering of hard degrees of freedom. This conclusion should also apply to gravitational scattering and to black hole formation and evaporation. In developing the classical scattering theory, we show that generic Lorenz gauge solutions fail to satisfy the matching condition on the vector potential at spatial infinity proposed by Strominger to define the field configuration space, and we suggest a way to remedy this. We also show that when soft degrees of freedom are present, the order at which nonlinearities first arise in the scattering map is second order in Lorenz gauge, but can be third order in other gauges.
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Finite temperature fermionic condensate and currents in topologically nontrivial spaces: We investigate the finite temperature fermionic condensate and the expectation values of the charge and current densities for a massive fermion field in a spacetime background with an arbitrary number of toroidally compactified spatial dimensions in the presence of a non-vanishing chemical potential. Periodicity conditions along compact dimensions are taken with arbitrary phases and the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm-like effects on the expectation values. They are periodic functions of magnetic fluxes enclosed by compact dimensions with the period equal to the flux quantum. The current density has nonzero components along compact dimensions only. Both low- and high-temperature asymptotics of the expectation values are studied. In particular, it has been shown that at high temperatures the current density is exponentially suppressed. This behavior is in sharp contrast with the corresponding asymptotic in the case of a scalar field, where the current density linearly grows with the temperature. The features for the models in odd dimensional spacetimes are discussed. Applications are given to cylindrical and toroidal nanotubes described within the framework of effective Dirac theory for the electronic subsystem.
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A non-commuting twist in the partition function: We compute a twisted index for an orbifold theory when the twist generating group does not commute with the orbifold group. The twisted index requires the theory to be defined on moduli spaces that are compatible with the twist. This is carried out for CHL models at special points in the moduli space where they admit dihedral symmetries. The commutator subgroup of the dihedral groups are cyclic groups that are used to construct the CHL orbifolds. The residual reflection symmetry is chosen to act as a `twist' on the partition function. The reflection symmetries do not commute with the orbifolding group and hence we refer to this as a non-commuting twist. We count the degeneracy of half-BPS states using the twisted partition function and find that the contribution comes mainly from the untwisted sector. We show that the generating function for these twisted BPS states are related to the Mathieu group M_{24}.
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Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect: Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two-- and higher--dimensional surfaces (being able to mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero depths). What we have considered is the {\it additional} contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.
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Thermoelectric Conductivities at Finite Magnetic Field and the Nernst Effect: We study the thermoelectric conductivities of a strongly correlated system in the presence of a magnetic field by the gauge/gravity duality. We consider a class of Einstein-Maxwell-Dilaton theories with axion fields imposing momentum relaxation. General analytic formulas for the direct current(DC) conductivities and the Nernst signal are derived in terms of the black hole horizon data. For an explicit model study, we analyse in detail the dyonic black hole modified by momentum relaxation. In this model, for small momentum relaxation, the Nernst signal shows a bell-shaped dependence on the magnetic field, which is a feature of the normal phase of cuprates. We compute all alternating current(AC) electric, thermoelectric, and thermal conductivities by numerical analysis and confirm that their zero frequency limits precisely reproduce our analytic DC formulas, which is a non-trivial consistency check of our methods. We discuss the momentum relaxation effects on the conductivities including cyclotron resonance poles.
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One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity: We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are rational functions of the momenta, also arise in the quantization of self-dual gravity in four-dimensional Minkowski space. Our ansatz agrees with explicit computations via D-dimensional unitarity cuts for n less than or equal to 6. It also has the expected analytic behavior, for all n, as a graviton becomes soft, and as two momenta become collinear. The gravity results are closely related to analogous amplitudes in (self-dual) Yang-Mills theory.
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Time Lumps in Nonlocal Stringy Models and Cosmological Applications: We study lump solutions in nonlocal toy models and their cosmological applications. These models are motivated by a description of D-brane decay within string field theory framework. In order to find cosmological solutions we use the simplest local approximation keeping only second derivative terms in nonlocal dynamics. We study a validity of this approximation in flat background where time lump solutions can be written explicitly. We work out the validity of this approximation. We show that our models at large time exhibit the phantom behaviour similar to the case of the string kink.
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N=2 Chiral Supergravity in (10 + 2)-Dimensions As Consistent Background for Super (2 + 2)-Brane: We present a theory of N=2 chiral supergravity in (10+2)-dimensions. This formulation is similar to N=1 supergravity presented recently using null-vectors in 12D. In order to see the consistency of this theory, we perform a simple dimensional reduction to ten-dimensions, reproducing the type IIB chiral supergravity. We also show that our supergravity can be consistent background for super (2+2)-brane theory, satisfying fermionic invariance of the total action. Such supergravity theory without manifest Lorentz invariance had been predicted by the recent F-theory in twelve-dimensions.
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Wilson loops in large N field theories: We propose a method to calculate the expectation values of an operator similar to the Wilson loop in the large N limit of field theories. We consider N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the area of a fundamental string worldsheet in certain supergravity backgrounds. We also consider the case of coincident M-theory fivebranes where one is lead to calculating the area of M-theory two-branes. We briefly discuss the computation for 2+1 dimensional super-Yang-Mills with sixteen supercharges which is non-conformal. In all these cases we calculate the energy of quark-antiquark pair.
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Generalized Poincare algebras and Lovelock-Cartan gravity theory: We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the generalized Poincar\'{e} algebra $\mathfrak{B}_{2n+1},$ while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern-Pontryagin character for the $B_{2n+1}$ group.
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Motivic Amplitudes and Cluster Coordinates: In this paper we study motivic amplitudes--objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf_n(P^3) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude A_{7,2} and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster X-coordinates on Conf_n(P^3). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to A_{7,2} being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster X-coordinates of a single algebra. In this respect it is similar to Abel's 5-term dilogarithm identity.
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Electron-positron pairs production in a macroscopic charged core: Classical and semi-classical energy states of relativistic electrons bounded by a massive and charged core with the charge-mass-radio Q/M and macroscopic radius R_c are discussed. We show that the energies of semi-classical (bound) states can be much smaller than the negative electron mass-energy (-mc^2), and energy-level crossing to negative energy continuum occurs. Electron-positron pair production takes place by quantum tunneling, if these bound states are not occupied. Electrons fill into these bound states and positrons go to infinity. We explicitly calculate the rate of pair-production, and compare it with the rates of electron-positron production by the Sauter-Euler-Heisenberg-Schwinger in a constant electric field. In addition, the pair-production rate for the electro-gravitational balance ratio Q/M = 10^{-19} is much larger than the pair-production rate due to the Hawking processes.
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Topological Conformal Algebra in $2d$ Gravity Coupled to Minimal Matter: An infinite number of topological conformal algebras with varying central charges are explicitly shown to be present in $2d$ gravity (treated both in the conformal gauge and in the light-cone gauge) coupled to minimal matter. The central charges of the underlying $N=2$ theory in two different gauge choices are generically found to be different. The physical states in these theories are briefly discussed in the light of the $N=2$ superconformal symmetry.
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Managing $γ_5$ in Dimensional Regularization II: the Trace with more $γ_5$: In the present paper we evaluate the anomaly for the abelian axial current in a non abelian chiral gauge theory, by using dimensional regularization. This amount to formulate a procedure for managing traces with more than one $\gamma_5$. \par The suggested procedure obeys Lorentz covariance and cyclicity, at variance with previous approaches (e.g. the celebrated 't Hooft and Veltman's where Lorentz is violated) \par The result of the present paper is a further step forward in the program initiated by a previous work on the traces involving a single $\gamma_5$. The final goal is an unconstrained definition of $\gamma_5$ in dimensional regularization. Here, in the evaluation of the anomaly, we profit of the axial current conservation equation, when radiative corrections are neglected. This kind of tool is not always exploited in field theories with $\gamma_5$, e.g. in the use of dimensional regularization of infrared and collinear divergences.
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Absence of the Gribov ambiguity in a quadratic gauge: The Gribov ambiguity exists in various gauges except algebraic gauges. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold $\mathbb{S}^3$, when a proper boundary condition on the gauge configuration is taken into account. Thus, providing one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the \tmem{BRST} invariance is preserved in this gauge.
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On the Quantum Origin of Structure in the Inflationary Universe: In this lecture I give a pedagogical introduction to inflationary cosmology with a special focus on the quantum generation of cosmological perturbations.
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Two loop five point integrals: light, heavy and large spin correlators: We evaluated all two loop conformal integrals appearing in five point correlation functions of protected operators of $\mathcal{N} = 4$ Super Yang-Mills in several kinematical regimes. Starting from the correlation function of the lightest operators of the theory, we were able to extract structure constants of up to two spinning operators for small and large values of polarizations and spin. We conjectured an universal all loop behaviour for the large spin small polarization structure constants and comment on the subtleties of analytically continuing it from finite to large spin. We also consider correlation functions of heavier operators that get factorized in the more fundamental object called decagon. We fixed this object at two loops in general kinematics and studied its physical properties under OPE and null limits.
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Orientifolds, RR Torsion, and K-theory: We analyze the role of RR fluxes in orientifold backgrounds from the point of view of K-theory, and demonstrate some physical implications of describing these fluxes in K-theory rather than cohomology. In particular, we show that certain fractional shifts in RR charge quantization due to discrete RR fluxes are naturally explained in K-theory. We also show that some orientifold backgrounds, which are considered distinct in the cohomology classification, become equivalent in the K-theory description, while others become unphysical.
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Towards a Non-Supersymmetric String Phenomenology: Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively little work studying the phenomenologies associated with their non-supersymmetric counterparts. The primary reason for this relative lack of attention is the fact that strings without spacetime supersymmetry are generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper, we demonstrate that this hurdle can be overcome in a class of tachyon-free four-dimensional string models realized through coordinate-dependent compactifications. Moreover, as we shall see, it is possible to construct models in this class whose low-lying states resemble the Standard Model (or even potential unified extensions thereof) --- all without any light superpartners, and indeed without supersymmetry at any energy scale. The existence of such models thus opens the door to general studies of non-supersymmetric string phenomenology, and in this paper we proceed to discuss a variety of theoretical and phenomenological issues associated with such non-supersymmetric strings. On the theoretical side, we discuss the finiteness properties of such strings, the general characteristics of their mass spectra, the magnitude and behavior of their one-loop cosmological constants, and their interpolation properties. By contrast, on the phenomenological side, the properties we discuss are more model-specific and include their construction techniques, their natural energy scales, their particle and charge assignments, and the magnitudes of their associated Yukawa couplings and scalar masses.
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Clock Fields and Logarithmic Decay of Dark Energy: We investigate the physical measurability of the infrared instability of a de Sitter phase in the formalism recently proposed by Kitamoto et al.. We find that the logarithmic decay of the effective cosmological constant is only measurable if an additional clock field is introduced.
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All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops: We give a closed-form, prescriptive representation of all-multiplicity two-loop MHV amplitude integrands in fully-color-dressed (non-planar) maximally supersymmetric Yang-Mills theory.
hep-th
Slowly rotating Einstein-Maxwell-dilaton black hole and some aspects of its thermodynamics: A slowly rotating black hole solution in Einstein-Maxwell-dilaton gravity was considered. Having used the obtained solution we investigated thermodynamic functions such as black hole's temperature, entropy and heat capacity. In addition to examine thermodynamic properties of the black hole extended technique was applied. The equation of state of Van der Waals type was obtained and investigated. It has been shown that the given system has phase transitions of the first as well as of the zeroth order for the temperatures below a critical one which is notable feature of the black hole. A coexistence relation for two phases was also considered and latent heat was calculated. In the end, critical exponents were calculated.
hep-th
Celestial Klein Spaces: We consider the analytic continuation of $(p+q)$-dimensional Minkowski space (with $p$ and $q$ even) to $(p,q)$-signature, and study the conformal boundary of the resulting "Klein space". Unlike the familiar $(-+++..)$ signature, now the null infinity ${\mathcal I}$ has only one connected component. The spatial and timelike infinities ($i^0$ and $i'$) are quotients of generalizations of AdS spaces to non-standard signature. Together, ${\mathcal I}, i^0$ and $i'$ combine to produce the topological boundary $S^{p+q-1}$ as an $S^{p-1} \times S^{q-1}$ fibration over a null segment. The highest weight states (the $L$-primaries) and descendants of $SO(p,q)$ with integral weights give rise to natural scattering states. One can also define $H$-primaries which are highest weight with respect to a signature-mixing version of the Cartan-Weyl generators that leave a point on the celestial $S^{p-1} \times S^{q-1}$ fixed. These correspond to massless particles that emerge at that point and are Mellin transforms of plane wave states.
hep-th
Twist Quantization of String and B Field Background: In a previous paper, we investigated the Hopf algebra structure in string theory and gave a unified formulation of the quantization of the string and the space-time symmetry. In this paper, this formulation is applied to the case with a nonzero B-field background, and the twist of the Poincare symmetry is studied. The Drinfeld twist accompanied by the B-field background gives an alternative quantization scheme, which requires a new normal ordering. In order to obtain a physical interpretation of this twisted Hopf algebra structure, we propose a method to decompose the twist into two successive twists and we give two different possibilities of decomposition. The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincare symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincare symmetry on the Moyal type noncommutative space.
hep-th
On string theory on AdS$_3\times {M}_7$ in the tensionless limit: We review old and recent results on a special limit of string theory on AdS$_3\times M_7$ with pure NS-NS fluxes: the limit in which the string length $\ell_s=\sqrt{\alpha'}$ equals the AdS$_3$ radius $R $. At this point of the moduli space, the theory exhibits special properties, which we discuss. Special attention is focused on features of correlation functions that are related to the non-compactness of the boundary CFT target space, and on how these features change when the point $k\equiv R^2/\alpha ' =1$ is approached. Also, we briefly review recent proposals for exact realizations of AdS/CFT correspondence at this special point. \[\] This is the transcript of the talk delivered by the author at the 8$^{\text{th}}$ edition of the Quantum Gravity in the Southern Cone conference, held in Patagonia, December 16$^{\text{th}}$ - 20$^{\text{th}}$, 2019.
hep-th
Release of physical modes from unphysical fields: We present a basic idea and a toy model that physical modes originate from unobservable fields. The model is defined on a higher-dimensional space-time and has fermionic symmetries that make fields unphysical, and observable modes can appear through a dimensional reduction.
hep-th