Black hole microstates in AdS

TL;DR

The paper extends a higher-dimensional Cardy-like framework to include angular momentum, $U(1)$ charge, and hyperscaling violation, showing that the Bekenstein-Hawking entropy of a wide class of AdS black branes, large AdS-Schwarzschild/ Kerr-type black holes, and D$p$-brane backgrounds can be understood as the microcanonical degeneracy of states in the dual CFT. Central to the construction is the AdS soliton as the ground state and the corresponding vacuum energy, which, together with modular properties and boosts, yields entropy formulas that reproduce bulk thermodynamics across dimensions. It also establishes universal aspects of the degeneracy, discusses the Hartman–Keller–Stoica universality in higher dimensions, and analyzes logarithmic corrections from both gravity and field theory viewpoints. The results provide a cohesive holographic counting framework for black hole microstates in AdS, linking Euclidean gravity, solitonic ground states, and high-temperature operator spectra in a broad set of backgrounds. The work highlights the pivotal role of vacuum energy and modularity as organizing principles for black hole entropy in diverse holographic theories and opens avenues for exploring charged, rotating, and hyperscaling-violating systems within a unified Cardy-like picture.

Abstract

We extend a recently derived higher-dimensional Cardy formula to include angular momenta, which we use to obtain the Bekensten-Hawking entropy of AdS black branes, compactified rotating branes, and large Schwarzschild/Kerr black holes. This is the natural generalization of Strominger's microscopic derivation of the BTZ black hole entropy to higher dimensions. We propose an extension to include $U(1)$ charge, which agrees with the Bekenstein-Hawking entropy of large Reissner-Nordstrom/Kerr-Newman black holes at high temperature. We extend the results to arbitrary hyperscaling violation exponent (this captures the case of black D$p$-branes as a subclass) and reproduce logarithmic corrections.