Probing the EVH limit of supersymmetric AdS black holes
Kevin Goldstein, Vishnu Jejjala, Yang Lei, Sam van Leuven, Wei Li
Abstract
A bstract 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 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.