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.
Highlights
A nontrivial entropy and carries both angular momentum and electric charge
Using holography we show that the free energy on S3 and the superconformal index of the dual three-dimensional N = 2 SCFT, in the planar limit, are related in a simple universal way
The general expectation is that the entropy of the black hole is captured by the degeneracy of states in the 3d SCFT which preserve the same amount of supersymmetry as the black hole and carry the same charges
Summary
The equations of motion (2.2) admit a spinning, electrically charged black hole solution [21] (see [22, 23]). The solution describes an AdS black hole with an outer and an inner horizon, provided m is larger than a critical value and a2 < 1 (see, e.g., [41]). Without loss of generality we can assume a ≥ 0, δ ≥ 0, m ≥ 0.5 The physical quantities characterizing the black hole are its energy E, electric charge Q, and angular momentum J, given by m E = G(4)Ξ2 cosh 2δ , m. Where β ≡ T −1 is the inverse temperature of the black hole and ΩH is the angular velocity of the horizon, given by.
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