We analyze AdS 5 black holes that are nearly supersymmetric. They depart from the BPS limit in two distinct ways: a temperature takes them above extremality and a potential maintains extremality but violates a certain constraint. We study the thermodynamics of these deformations and their interplay in detail. We discuss recent microscopic computations of BPS black hole entropy in N = 4 SYM and generalize the arguments to the nearBPS regime by relaxing constraints imposed by supersymmetry. Our methods recover gravitational results from microscopic theory also for nearBPS black holes.

We construct the dilaton potential in the gravity dual theory of AdS/QCD for the warp factor of Refs. [1,2]. Using this AdS 5 -metric with properties similar to QCD, we find that the gravity dual leads to a meaningful gauge coupling in the region between the charmonium and bottonium mass, but differs slightly from QCD in the extreme UV. When we fix the ultraviolet behavior in accord with the β-function, we can obtain good agreement with the overall heavy quark-antiquark potential. Although the leading order proportional to − α 4/3 r differs from perturbative QCD, the full potential agrees quite well with the short distance QCD potential in NNLO.

We employ supersymmetric localization to determine the exact partition function of 3d N " 2 gauge theories on a background given by a round S 2 fibered over a circle and certain complexified background fields. The Coulomb branch localization locus includes monopole configurations, and the partition function reduces to a matrix model. We consider the partition function of the ABJM theory on this background as an explicit case. We verify that the large-N limit of the ABJM theory partition function produces, in the Cardy limit, the entropy function of the dual rotating, electrically charged asymptotically AdS 4 supersymmetric black holes and thus provides a microscopic explanation for the Bekenstein-Hawking entropy.

We compute the Rényi entropy and the supersymmetric Rényi entropy for the six-dimensional free (2, 0) tensor multiplet. We make various checks on our results, and they are consistent with the previous results about the (2, 0) tensor multiplet. As a by-product, we have established a canonical way to compute the Rényi entropy for p-form fields in d-dimensions.

Clustering of like-sign vortices in a planar bounded domain is known to occur at negative temperature, a phenomenon that Onsager demonstrated to be a consequence of bounded phase space. In a confined superfluid, quantized vortices can support such an ordered phase, provided they evolve as an almost isolated subsystem containing sufficient energy. A detailed theoretical understanding of the statistical mechanics of such states thus requires a microcanonical approach. Here we develop an analytical theory of the vortex clustering transition in a neutral system of quantum vortices confined to a two-dimensional disk geometry, within the microcanonical ensemble. The choice of ensemble is essential for identifying the correct thermodynamic limit of the system, enabling a rigorous description of clustering in the language of critical phenomena. As the system energy increases above a critical value, the system develops global order via the emergence of a macroscopic dipole structure from the homogeneous phase of vortices, spontaneously breaking the Z 2 symmetry associated with invariance under vortex circulation exchange, and the rotational SO(2) symmetry due to the disk geometry. The dipole structure emerges characterized by the continuous growth of the macroscopic dipole moment which serves as a global order parameter, resembling a continuous phase transition. The critical temperature of the transition, and the critical exponent associated with the dipole moment, are obtained exactly within mean-field theory. The clustering transition is shown to be distinct from the final state reached at high energy, known as supercondensation. The dipole moment develops via two macroscopic vortex clusters and the cluster locations are found analytically, both near the clustering transition and in the supercondensation limit. The microcanonical theory shows excellent agreement with Monte Carlo simulations, and signatures of the transition are apparent even for a modest system of 100 vortices, accessible in current Bose-Einstein condensate experiments.

Localization of supersymmetric N = 2 Chern-Simons-Matter theory on a squashed S 3 with SU(2) × U(1) isometry has been studied by different groups of authors. In this paper, we localize the theory on a squashed S 3 with SU(2) × U(1) isometry and a class of complex background. We see that certain kinds of shifts of the background gauge fields are crucial in obtaining nontrivial results, and the previously found results on this manifold can be incorporated in our results as special limits.

Using $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS5 black holes including both the outer and the inner horizons with their corresponding entropy and energy. This $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory approach to black hole thermodynamics leads to an effective CFT2 interpretation similar to the work by Callan and Maldacena. We corroborate this effective CFT2 by implementing a particular near-horizon limit that geometrizes the Virasoro algebras as asymptotic symmetries. Using the effective CFT2 picture, we discuss aspects of the Hawking radiation rate for a region of the near-extremal AdS5 black hole quantum evolution.

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS4,5,6,7 BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions.