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

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.
SISSA, Via Bonomea 265, 34136 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy, ICTP, Strada Costiera 11, 34151 Trieste, Italy, Dipartimento di Fisica, Universit`a di Milano-Bicocca, I-20126 Milano, Italy, INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy
General Relativity and Quantum Cosmology