Dualities in D=5, N=2 Supergravity, Black Hole Entropy, and AdS Central Charges

TL;DR

This paper explores black hole microstate counting in D=5, N=2 supergravity, demonstrating duality invariances and matching statistical entropy calculations with thermodynamic results using AdS/CFT techniques.

Contribution

It introduces a duality invariance connecting black holes and black strings and applies AdS_2 and AdS_3 central charge methods for entropy calculations.

Findings

Perfect agreement between statistical and thermodynamical entropy.

Duality invariance relates electrically charged black holes and magnetically charged black strings.

Microscopic entropy calculations using Brown-Henneaux central charges are validated.

Abstract

The issue of microstate counting for general black holes in D=5, N=2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS_2. Furthermore, we show that the considered supergravity theory enjoys a duality invariance which connects electrically charged black holes and magnetically charged black strings. The near-horizon geometry of the latter turns out to be AdS_3 x S^2, which allows a microscopic calculation of their entropy using the Brown-Henneaux central charges in Cardy's formula. In both approaches we find perfect agreement between statistical and thermodynamical entropy.