Holographic Thermal Observables and M2-branes

TL;DR

This paper combines holography and supersymmetric localization to compute thermal observables for 3d N=2 SCFTs on M2-branes, providing new results for free energy, Casimir energy, and large temperature behavior.

Contribution

It introduces a novel holographic approach to calculate thermal observables in 3d SCFTs and proposes a conjecture for their large temperature expansion structure.

Findings

Computed thermal free energy density on S^1 x R^2

Derived Casimir energy on T^2 x R

Identified leading coefficients in large temperature free energy expansion

Abstract

We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d $\mathcal{N}=2$ holographic SCFTs arising on the worldvolume of $N$ M2-branes. We obtain results for the thermal free energy density on $S^1 \times \mathbb{R}^2$, the Casimir energy on $T^{2} \times \mathbb{R}$, and the three leading coefficients in the large temperature limit of the free energy on $S^1\times S^2$ valid to subleading order in the large $N$ limit. As a byproduct of our holographic analysis we also present a conjecture for the structure of the large temperature expansion of the thermal free energy of general 3d CFTs on $S^1\times S^2$.