We evaluate the large-N behavior of the superconformal indices of toric quiver gauge theories, and use it to find the entropy functions of the dual electrically charged rotating AdS 5 black holes. To this end, we employ the recently proposed Bethe Ansatz method, and find a certain set of solutions to the Bethe Ansatz Equations of toric theories. This, in turn, allows us to compute the large-N behavior of the index for these theories, including the infinite families Y pq , X pq and L pqr of quiver gauge theories. Our results are in perfect agreement with the predictions made recently using the Cardy-like limit of the superconformal index. We also explore the index structure in the space of chemical potentials and describe the pattern of Stokes lines arising in the conifold theory case.

We study several cases of IR enhancements of global symmetry in four dimensions. In particular, we consider a sequence of Spin(n + 4) supersymmetric gauge theories (8 ≥ n ≥ 1) with n vectors and spinor matter with 32 components. We show that the subgroup of the flavor symmetry of these theories rotating the matter in the spinor representations in the UV, when proper gauge singlet fields are added, enhances to the commutant of SU (2) in E 9−n . We discuss several other interesting cases of enhanced symmetries and the interplay between symmetry enhancement and self-duality. We also make some observations about possible interconnections between chiral ring relations and symmetry enhancement. Finally, we conjecture relations of the discussed models to compactifications of certain conformal matter models in six dimensions on tori. The conjecture is based on deriving a relation between five dimensional models with Spin gauge groups and conformal theories in six dimensions. As a by product of our considerations we discover a new instance of a simple self-duality of a theory with an SU (6) gauge group. arXiv:1809.00541v1 [hep-th] 3 Sep 2018

We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard lmω modes of the scalar field (those associated with a spherical harmonic Y lm and a temporal mode e −iωt ), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external lmω modes of the field. They allow the computation of < Φ 2 >ren and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally-coupled massless scalar field (which is non-conformal), relating it to the d'Alembertian of < Φ 2 >ren. This expression proves itself useful in various calculations of the renormalized stress-energy tensor. I. INTRODUCTIONIn the framework of semiclassical general relativity, the gravitational field is treated classically as a curved spacetime while other fields are treated as quantum fields residing in this background spacetime. The relation between the spacetime geometry and the stress-energy of the quantum fields is described by the semiclassical Einstein equation( 1.1) where G µν is the Einstein tensor of spacetime, and ren is the renormalized stress-energy tensor (RSET), which is the renormalized expectation value of the stress-energy tensor operatorT , associated with the quantum fields. In Eq. (1.1) and throughout this paper we adopt standard geometric units c = G = 1, and signature (− + ++).The main challenge in analyzing the semiclassical Einstein equation is the computation of the RSET. Even when the background geometry is fixed and the corresponding metric is given, performing a procedure of renormalization is not an easy task. The task becomes much more difficult upon trying to solve the full self-consistent problem represented by Eq. (1.1). One reason (besides the obvious numerical challenge) is that Eq. (1.1) admits runaway solutions [1].An example of a quantum field that is often chosen for its simplicity is that of a scalar field, which satisfies the Klein-Gordon equationwhereΦ is the scalar field operator, m denotes the field's mass, and ξ is the coupling constant. As a first stage towards calculating the RSET, it is customary to begin by calculating <Φ 2 > ren , as this quantity is endowed with many of the essential features of the RSET, but is simpler to compute. In other words, <Φ 2 > ren serves as a simple toy model for the RSET. The standard method to calculate quantities which are quadratic in the field and its derivatives is point-splitting (or covariant point ...

We analyze the late-time decay of scalar perturbations in extremal Reissner-Nordstrom spacetime. We consider individual spherical-harmonic modes l of a test massless scalar field, restricting our attention to initial data of compact support, with generic regular behavior across the horizon. We obtain a decay rate ∝ t −(2l+3) (just like in Schwarzschild) for incident waves scattered by the black hole. However, for waves originating at the horizon's neighborhood we obtain a slightly slower decay, ∝ t −(2l+2) . We discuss relations to previous works.

We study two cases of interrelations between the enhancement of symmetries in the infrared (IR) and duality properties of supersymmetric quantum field theories in four dimensions. First, we discuss an SU(2) N=1 model with four flavors, singlet fields, and a superpotential. We show that this model flows to a conformal field theory with E_{6}×U(1) global symmetry. The enhancement of the flavor symmetry follows from Seiberg duality. The second example is concerned with an SU(4) gauge theory with matter in the fundamental and antisymmetric representations. We argue that this model has enhanced SO(12) symmetry in the IR, and, guided by this enhancement, we deduce a new IR duality.