Finite temperature CFT results for all couplings: O(N) model in 2+1 dimensions

Abstract

A famous example of gauge/gravity duality is the result that the entropy density of strongly coupled $\mathcal{N}=4$ SYM in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at finite temperature $T$ for all couplings $\lambda$ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at $\lambda =0$ to exactly 4/5 of the Stefan-Boltzmann limit at $\lambda =\infty$. Calculating the retarded energy-momentum tensor correlator in the scalar channel at $\lambda =\infty$, I find that it has two logarithmic branch cuts originating at $\omega =\pm 4T\ln \frac{1+\sqrt{5}}{2}$, but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic CFTs in 2+1 dimensions.

Comments: 5 pages, 1 figure; v2: typos fixed, new section on universality of 4/5 ratio; v3: matches published version; v4: typos/errors corrected