On the free-energy of three-dimensional CFTs and polylogarithms

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.