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Finite temperature CFT results for all couplings: O(N) model in 2+1 dimensions
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abstract
A famous example of gauge/gravity duality is the result that the entropy density of strongly coupled ${\cal N}=4$ 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 $\omega=\pm 4 T \ln \frac{1+\sqrt{5}}{2}$, 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.
Forward citations
Cited by 4 Pith papers
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Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling
For QED in 2+1 dimensions with many fermion flavors, the thermal pressure to next-to-leading order in 1/Nf is computed across all couplings, giving a curve bounded by the free-fermion and free-photon pressures.
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Thermal field theory correlators in the large-$N$ limit and the spectral duality relation
The spectral duality relation, previously found for 3d CFTs and 4d black holes, is shown to hold for meromorphic thermal two-point correlators in any dimension and for correlators related by double-trace deformations,...
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On the negative coupling O(N) model in 2d at high temperature
For the 2d negative-coupling O(N) model at large N, the correct vacuum is a saddle point on a non-principal Riemann sheet, giving a real free energy and dynamical stability at all temperatures.
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Large charge at large N
A saddle-point evaluation of the O(2N) Wilson-Fisher partition function yields the large-charge conformal dimension and finite-temperature free energy in the regime 1 << N << Q, including the universal Q^0 Casimir term.
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