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 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.

AdS black holes, holography and localization

“…The case of AdS 6 and AdS 7 have been analysed in , Kantor et al (2020) and Nahmgoong (2019). Other interesting developments can be found in , Bobev and Crichigno (2019) and Goldstein et al (2020).…”

Gravitational Cardy limit and AdS black hole entropy

“…Horizon (EVH) limit discussed in [24] (see also [25][26][27][28]). For asymptotically AdS d+1 BPS black holes, the authors of [24] related the boundary CFT d and the corresponding nearhorizon computations in the EVH limit. In this case, there arises an effective 2d CFT obtained in the near-horizon region.…”

“…and for the graviton, we have We can truncate this solution as constructed in [51], where the two charges and angular momenta are set equal. This truncation can be done by letting X = X 1 = X 2 = e −ϕ/ √ 10 , ϕ 2 = 0 and A (1) = A 1 (1) = A 2 (1) and the Lagrangian of interest becomes 23) and the equations of motion are 24) and for the graviton…”

The large-N limit of the 4d $$ \mathcal{N} $$ = 1 superconformal index

“…This would lead us slightly off the supersymmetric sector that is captured by the index. Related to this idea, interesting progress has been reported on near-extremal limits of black hole solutions in[45][46][47].…”