The Minimal Landau Background Gauge on the Lattice

TL;DR

This paper introduces the first numerical implementation of the minimal Landau background gauge for lattice Yang-Mills theory, applicable to any SU(N) group, and demonstrates its effectiveness through preliminary tests.

Contribution

It generalizes the minimal Landau gauge to include background fields on the lattice, enabling new numerical studies of gauge theories.

Findings

Convergence similar to the null background case.

Applicable to general SU(N) gauge groups.

Preliminary tests in 4D SU(2) show promising results.

Abstract

We present the first numerical implementation of the minimal Landau background gauge for Yang-Mills theory on the lattice. Our approach is a simple generalization of the usual minimal Landau gauge and is formulated for general SU(N) gauge group. We also report on preliminary tests of the method in the four-dimensional SU(2) case, using different background fields. Our tests show that the convergence of the numerical minimization process is comparable to the case of a null background. The uniqueness of the minimizing functional employed is briefly discussed.