The large N limit of topologically twisted indices: a direct approach
Seyed Morteza Hosseini, Alberto Zaffaroni
Abstract
A bstract We study the large N limit of the refined topologically twisted index of three-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 × S 7 black holes.