Abstract
We study a supersymmetric, rotating, electrically charged black hole in AdS4 which is a solution of four-dimensional minimal gauged supergravity. Using holography we show that the free energy on S3 and the superconformal index of the dual three-dimensional mathcal{N} = 2 SCFT, in the planar limit, are related in a simple universal way. This result applies to large classes of SCFTs constructed from branes in string and M-theory which we discuss in some detail. For theories of class mathcal{R} , which arise from N M5-branes wrapped on hyperbolic three-manifolds, we show that the superconformal index agrees with the black hole entropy in the large N limit.
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