Thermodynamics of Near BPS Black Holes in AdS$_4$ and AdS$_7$

TL;DR

This work develops the thermodynamics of near-BPS black holes in AdS$_4$ and AdS$_7$, identifying two orthogonal deformations away from the BPS surface and their interplay with BPS constraints. It constructs a near-BPS framework by generalizing boundary conditions on microscopic states and demonstrates a precise match between gravitational thermodynamics and microscopic entropy calculations in both dimensions. The authors introduce a height function $h$ to quantify departures from the BPS surface, derive a quadratic mass formula with a near-BPS potential $\varphi$, and show that near-BPS entropy and response coefficients $C_T$ and $C_E$ align with holographic expectations. The results provide a unified, UV-complete perspective on near-BPS black holes via entropy extremization, the nAdS$_2$/CFT$_1$ viewpoint, and a consistent mapping between gravitational potentials and microscopic fugacities, with implications for universality and holographic duals of near-supersymmetric systems.

Abstract

We develop the thermodynamics of black holes in AdS$_4$ and AdS$_7$ near their BPS limit. In each setting we study the two distinct deformations orthogonal to the BPS surface as well as their nontrivial interplay with each other and with BPS properties. Our results illuminate recent microscopic calculations of the BPS entropy. We show that these microscopic computations can be leveraged to also describe the near BPS regime, by generalizing the boundary conditions imposed on states.

Figures (1)

• Figure 1: Gibbs' free energy $G$ of the non-rotating AdS$_4$ black hole. The upper left corner is the BPS limit where $\Phi^2-\Phi^2_*=T=0$ and $G=0$. The rest of the plot has positive potentials $\Phi^2-\Phi^2_*, T$ and the free energy $G<0$.