Holographic thermal observables and M2-branes

Abstract

We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d $$ \mathcal{N} $$ N = 2 holographic SCFTs arising on the worldvolume of N M2-branes. We obtain results for the thermal free energy density on S1 × ℝ2, the Casimir energy on T2 × ℝ, and the three leading coefficients in the large temperature limit of the free energy on S1 × 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 × S2.

Large N superconformal indices for 3d holographic SCFTs

“…Another important application of the results above is in the holographic calculation of thermal observables in 3d N = 2 holographic SCFTs beyond the strict large N limit. As recently demonstrated in [65] the result in (4.14) can be used to calculate the thermal free energy on S 1 × R 2 as well as some coefficients in the thermal effective action on S 1 × S 2 for theories arising from M2-branes to order N 1 2 . The results of [65] can be directly applied, in conjunction with (4.14), in order to compute these observables also for all theories in Table 1.…”