| Summary: | Abstract Extremal black holes in general dimensions are well known to contain an AdS2 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 AdS2 factor lifts to a locally AdS3 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 1/16th BPS asymptotically AdS5 black hole, whose EVH limit has an AdS3 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 CFT4 to understand the emergence of a CFT2 in the IR of the CFT4, which is the field theory dual to the emergence of the locally AdS3 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 CFT2. Finally, we examine the EVH limit of supersymmetric black holes in other dimensions.
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