AdS7 black holes and holography

초록

We present a detailed study of the regularized on-shell action of the recently found asymptotically AdS7 black hole supergravity solution with three angular momenta and two electric charges. We show that a particular choice of finite counterterms in the holographic renormalization procedure yields a result for the on-shell action of the supersymmetric limit of the black hole solution which is in perfect agreement with the large N limit of the superconformal index of the dual 6d N = (2, 0) AN SCFT on S1 × S5. We also discuss a generalization of this 7d supergravity background to a new general family of black holes with horizons given by the Lp,q,r 5d Sasaki-Einstein manifolds. The regularized on-shell action of these new 7d black holes is also in agreement with supersymmetric localization results for the 6d N = (2, 0) SCFT on S1 × Lp,q,r. Finally, we briefly discuss a generalization of known AdS5 gauged supergravity backgrounds to new 5d black holes with L(p, q) lens space horizon topologies.

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