Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions

A famous example of gauge-gravity duality is the result that the entropy density of the strongly coupled N=4 supersymmetric Yang-Mills theory 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 a finite-temperature T for all couplings λ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at λ=0 to exactly 4/5 of the Stefan-Boltzmann limit at λ=∞. Calculating the retarded energy-momentum tensor correlator in the scalar channel at λ=∞, I find that it has two logarithmic branch cuts originating at ω=±4Tln(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 conformal field theories in 2+1 dimensions.