Holographic thermal observables and M2-branes

We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 holographic SCFTs arising on the worldvolume of N M2-branes. We obtain results for the thermal free energy density on S1 x Double-struck capital R2, the Casimir energy on T2 x Double-struck capital R, and the three leading coefficients in the large temperature limit of the free energy on S1 x S2 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 S1 x S2.