Superconformal indices at large $N$ and the entropy of AdS$_5$ $\times$ SE$_5$ black holes

Understand

The large $N$ limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS$_5$ 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 $\mathcal{N}=1$ four-dimensional conformal theories with a holographic dual.
• We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large $N$.
• For $\mathcal{N}=4$ SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS$_5 \times S^5$ for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates.