Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT

TL;DR

This paper explores the phase structure of BPS black holes in AdS space with equal electric charges, revealing sharp phase transitions and a perfect match between gravity and dual CFT descriptions.

Contribution

It provides a detailed analysis of the phase diagram for supersymmetric BPS black holes in AdS, connecting gravity variables with dual CFT variables and elucidating the supergravity constraint.

Findings

Identified sharp phase transitions in BPS black holes

Revealed a natural supergravity constraint in the dual CFT

Achieved a perfect match between gravity and CFT charges

Abstract

Using the general framework developed in hep-th/0607056, we study in detail the phase space of BPS Black Holes in AdS, for the case where all three electric charges are equal. Although these solitons are supersymmetric with zero Hawking temperature, it turns out that these Black Holes have rich phase structure with sharp phase transitions associated to a corresponding critical generalized temperature. We are able to rewrite the gravity variables in terms of dual CFT variables and compare the gravity phase diagram with the free dual CFT phase diagram. In particular, the elusive supergravity constraint characteristic of these Black Holes is particulary simple and in fact appears naturally in the dual CFT in the definition of the BPS Index. Armed with this constraint, we find perfect match between BH and free CFT charges up to expected constant factors.