On the Leading Order Term of the Lattice Yang-Mills Free Energy

TL;DR

This paper refines the understanding of the leading order term of the free energy in lattice Yang-Mills theory by explicitly characterizing a key boundary condition contribution, enabling precise calculations.

Contribution

It provides an explicit characterization and computation method for the boundary condition contribution to the free energy in lattice Yang-Mills theory.

Findings

Explicit formula for the leading order free energy term.

Characterization of the boundary condition contribution $K_d$.

Method for computing $K_d$ explicitly.

Abstract

In \cite{Cha1}, the leading order term of the free energy of $\text{U(N)}$ lattice Yang-Mills theory in $\Lambda_n=\{0,\ldots,n\}^d\subset \mathbb{Z}^d$ was determined, for every $N\geq 1$ and $d\geq 2$. The formula is explicit apart from a contribution $K_d$ which corresponds to the limiting free energy of lattice Maxwell theory with boundary conditions induced by the axial gauge. By suitably adjusting the boundary conditions, we provide an equivalent characterization of $K_d$ that admits its explicit computation.