Volume reduction through perturbative Wilson loops

TL;DR

This paper derives the perturbative expansion of Wilson loops in SU(N) lattice gauge theory with twisted boundary conditions, showing how volume independence is approached at large N and quantifying deviations at finite N.

Contribution

It provides explicit formulas for Wilson loops up to order g^4 in a twisted boundary setting, advancing understanding of volume dependence in lattice gauge theories.

Findings

Thermodynamic limit achieved at infinite N for any lattice size.

Quantitative measures of volume dependence at finite N.

Explicit perturbative expressions for Wilson loops up to g^4.

Abstract

We derive the perturbative expansion of Wilson loops to order g^4 in a SU(N) lattice gauge theory with twisted boundary conditions. Our expressions show that the thermodynamic limit is attained at infinite N for any number of lattice sites and allow to quantify the deviations from volume independence at finite large N as a function of the twist.