The large N limit of topologically twisted indices: a direct approach

We study the large N limit of the refined topologically twisted index of three-dimensional N = 2 gauge theories with a holographic dual, which is relevant for counting the number of microstates of rotating, magnetically charged and twisted AdS(4) black holes. As a difference with previous computations, we perform a direct saddle point analysis of the relevant matrix model. Among other things we explicitly identify the distribution of gauge magnetic fluxes that contributes at large N. The index exhibits a large N factorized form in agreement with the supergravity expectations based on gravitational blocks and correctly reproduces the entropy of magnetically charged rotating AdS(4) x S-7 black holes.