Large N Partition Functions, Holography, and Black Holes

We present a simple closed form expression for the topologically twisted index of the ABJM theory as a function of the magnetic fluxes and complex chemical potentials valid at fixed k and to all orders in the 1/N expansion. This in turn leads to analytic expressions for the topologically twisted index at fixed genus in the 't Hooft limit to all orders in the 1/sqrt[λ] expansion. These results have important implications for holography and the microscopic entropy counting of supersymmetric static AdS_{4} black holes. Generalizations to other SCFTs arising from M2-branes are also briefly discussed.