Background field technique and renormalization in lattice gauge theory

TL;DR

This paper proves that lattice gauge theory with a background field remains renormalizable at all perturbation orders without extra counterterms, using symmetry-based arguments similar to those in continuum regularization.

Contribution

It extends the renormalization proof to lattice gauge theories with background fields, showing no additional counterterms are needed beyond standard ones.

Findings

Renormalizability holds to all orders in perturbation theory.

No new counterterms are required for background fields.

The proof uses BRS, background gauge, and shift symmetries.

Abstract

Lattice gauge theory with a background gauge field is shown to be renormalizable to all orders of perturbation theory. No additional counterterms are required besides those already needed in the absence of the background field. The argument closely follows the treatment given earlier for the case of dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS, background gauge and shift symmetries of the lattice functional integral.