AdS7 black holes and holography

A bstract We present a detailed study of the regularized on-shell action of the recently found asymptotically AdS 7 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) A N SCFT on S 1 × S 5 . We also discuss a generalization of this 7d supergravity background to a new general family of black holes with horizons given by the L p , 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 S 1 × L p , q , r . Finally, we briefly discuss a generalization of known AdS 5 gauged supergravity backgrounds to new 5d black holes with L ( p , q ) lens space horizon topologies.