Probing the EVH limit of supersymmetric AdS black holes

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${}^{\mathrm{th}}$ 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.

46 pages; v2 reference added, typos corrected