Superconformal indices at large N and the entropy of AdS5 × SE5 black holes

Abstract

The large N limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS5 black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large N with arbitrary chemical potentials for all charges and angular momenta, for general N = 1 four-dimensional conformal theories with a holographic dual. We con-jecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large N. For N = 4 SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS5 × S5 for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS5 × SE5, where SE5 is a Sasaki-Einstein manifold. We first check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS5 × T 1,1, charged under the baryonic symmetry of the conifold theory and with equal angular mo-menta. We compute the entropy of these black holes using the attractor mechanism and we find complete agreement with the field theory predictions.