Large N superconformal indices for 3d holographic SCFTs

We study a limit of the superconformal index of the ABJM theory on S-1 x S-2 in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the 1/N expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d N = 4 SYM coupled to one adjoint and N-f fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS(4).