Half-BPS Geometries and Thermodynamics of Free Fermions

TL;DR

This paper explores the thermodynamic properties of half-BPS geometries in type IIB supergravity, modeled by free fermions, and analyzes their mass, entropy, and phase behavior at different temperatures.

Contribution

It provides a detailed analysis of thermodynamic regimes of half-BPS geometries linked to free fermions, including mass calculations and entropy matching.

Findings

ADM mass matches fermion thermal energy at low and high temperatures

Low temperature solutions have naked null singularities with potential horizon formation

High temperature solutions resemble dilute D3 brane gases

Abstract

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the "bubbling AdS" construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.