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 $S^1\times S^2$.
Categories: hep-th