On the Free-Energy of Three-Dimensional CFTs and Polylogarithms

Abstract

We study the O(N) vector model and the U(N) Gross-Neveu model with fixed total fermion number, in three dimensions. Using non-trivial polylogarithmic identities, we calculate the large-N renormalized free-energy density of these models, at their conformal points in a ``slab'' geometry with one finite dimension of length L. We comment on the possible implications of our results.

Latex, 13 pages, 2 eps figures; v2 typos corrected; v3 Expanded discussion of the results, added references

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Cited by in corpus (9)

• The Thermal Free Energy in Large N Chern-Simons-Matter Theories
• Evaluating the AdS dual of the critical O(N) vector model
• On the thermodynamics of the 2+1 dimensional Gross-Neveu model with complex chemical potential
• $3d$ fermion-boson map with imaginary chemical potential
• The fermion-boson map for large d
• Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential
• Quasi-particle re-summation and integral gap equation in thermal field theory
• Lee-Yang edge singularity in the three-dimensional Gross-Neveu model at finite temperature
• Noncritical M-theory and the Gross-Neveu model in 2+1 dimensions