Probing the EVH limit of supersymmetric AdS black holes

TL;DR

This paper investigates the EVH limit of supersymmetric AdS black holes, revealing an emergent AdS3/CFT2 structure in the near-horizon geometry and connecting it to the dual CFT via the superconformal index and Cardy formula.

Contribution

It demonstrates the emergence of a locally AdS3 factor in the EVH limit of supersymmetric AdS black holes and links this to the IR behavior of the dual CFT4 through the superconformal index.

Findings

Emergence of AdS3 geometry in EVH limit of BPS black holes.

Connection between superconformal index and CFT2 Cardy formula.

Extension of EVH analysis to black holes in various dimensions.

Abstract

Extremal black holes in general dimensions are well known to contain an AdS$_2$ factor in their near-horizon geometries. If the extremal limit is taken in conjunction with a specific vanishing horizon limit, the so-called Extremal Vanishing Horizon (EVH) limit, the AdS$_2$ factor lifts to a locally AdS$_3$ factor with a pinching angular direction. In this paper, we study the EVH limit of asymptotically AdS black holes which preserve some supersymmetry. The primary example we consider is the 1/16$^{\rm th}$ BPS asymptotically AdS$_5$ black hole, whose EVH limit has an AdS$_3$ factor in its near-horizon geometry. We also consider the near-EVH limit of this black hole, in which the near-horizon geometry instead contains an extremal BTZ factor. We employ recent results on the large-$N$ limit of the superconformal index of the dual CFT$_4$ to understand the emergence of a CFT$_2$ in the IR of the CFT$_4$, which is the field theory dual to the emergence of the locally AdS$_3$ factor in the near-horizon geometry. In particular, we show that the inverse Laplace transform of the superconformal index, yielding the black hole entropy, becomes equivalent to the derivation of a Cardy formula for the dual CFT$_2$. Finally, we examine the EVH limit of supersymmetric black holes in other dimensions.