Large N partition functions of 3d holographic SCFTs

Abstract

Abstract We study the S1 × $$ {\Sigma}_{\mathfrak{g}} $$ Σ g topologically twisted index and the squashed sphere partition function of various 3d $$ \mathcal{N} $$ N ≥ 2 holographic superconformal field theories arising from M2-branes. Employing numerical techniques in combination with well-motivated conjectures we provide compact closed-form expressions valid to all orders in the perturbative 1/N expansion for these observables. We also discuss the holographic implications of our results for the topologically twisted index for the dual M-theory Euclidean path integral around asymptotically AdS4 solutions of 11d supergravity. In Lorentzian signature this leads to a prediction for the corrections to the Bekenstein-Hawking entropy of a class of static asymptotically AdS4 BPS black holes.