# Renormalization of gauge theories in the background-field approach

## TL;DR

This paper demonstrates that gauge invariance is maintained during renormalization in a wide range of gauge theories using the background-field method, including gravity and non-relativistic models, by analyzing the BRST structure of counterterms.

## Contribution

It generalizes and strengthens existing results by showing gauge invariance preservation in diverse gauge theories through the background-field approach and BRST symmetry analysis.

## Key findings

- Gauge invariance preserved in renormalization of broad gauge theories.
- BRST structure of counterterms established for various models.
- Applicability to both relativistic and non-relativistic theories.

## Abstract

Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.