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.