The leading term of the Yang-Mills free energy

TL;DR

This paper derives an explicit formula for the leading term of the free energy in 3D U(N) lattice gauge theory as the lattice spacing approaches zero, introducing a novel proof technique that bypasses phase cell renormalization.

Contribution

It provides a new explicit formula for the free energy's leading term and introduces a novel proof method applicable to 3D and weakly coupled 4D theories.

Findings

Explicit formula for 3D U(N) free energy leading term

Novel proof technique avoiding phase cell renormalization

Formula applicability in weak coupling limit for 4D theory

Abstract

This article gives an explicit formula for the leading term of the free energy of three-dimensional $U(N)$ lattice gauge theory for any $N$, as the lattice spacing tends to zero. The proof is based on a novel technique that avoids phase cell renormalization. The technique also yields a similar formula for the four-dimensional theory, but only in the weak coupling~limit.