Large $N$ Partition Functions of 3d Holographic SCFTs

We study the $S^1\times {\mathrm{\Sigma }}_{\mathfrak{g}}$ topologically twisted index and the squashed sphere partition function of various 3d $\mathcal{N}\ge 2$ 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 $1\mathrm{/}N$ 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 AdS${}_4$ 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 AdS${}_4$ BPS black holes.