First order formulation of the Yang-Mills theory in a background field

TL;DR

This paper demonstrates the all-order renormalizability of the first order formulation of Yang-Mills theory in a background field using BRST identities, with a focus on background symmetry and renormalization techniques.

Contribution

It provides an iterative proof of renormalizability for the background gauge formulation of Yang-Mills theory employing BRST symmetry and recursive rescaling methods.

Findings

Proves renormalizability to all orders in perturbation theory.

Develops a recursive method involving field rescalings and mixings.

Establishes a renormalized effective action for background field theory.

Abstract

The background gauge renormalization of the first order formulation of the Yang-Mills theory is studied by using the BRST identities. Together with the background symmetry, these identities allow for an iterative proof of renormalizability to all orders in perturbation theory. However, due to the fact that certain improper diagrams which violate the BRST symmetry should be removed, the renormalizability must be deduced indirectly. The recursive method involves rescalings and mixings of the fields, which lead to a renormalized effective action for the background field theory.