Holographic thermal observables and M2-branes

A bstract We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d N = 2 holographic SCFTs arising on the worldvolume of N M2-branes. We obtain results for the thermal free energy density on S 1 × ℝ 2 , the Casimir energy on T 2 × ℝ , and the three leading coefficients in the large temperature limit of the free energy on S 1 × 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 × S 2 .