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

TL;DR

This paper calculates the large-N free-energy density of 3D conformal field theories, specifically the O(N) vector and Gross-Neveu models, using polylogarithmic identities, with potential implications for understanding their thermodynamic properties.

Contribution

It introduces a novel application of polylogarithmic identities to compute the free-energy of 3D CFTs at large N in a slab geometry.

Findings

Derived explicit formulas for free-energy density at conformal points

Identified polylogarithmic identities relevant to these models

Discussed potential implications for conformal field theory

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.