Renormalization trasformations of the 4D BFYM theory

TL;DR

This paper investigates the renormalization transformations in 4D BF-Yang-Mills theory, focusing on BRST cohomology and the potential to interpret Yang-Mills as a deformation of topological BF theory, aiding future perturbative analyses.

Contribution

It analyzes the most general renormalization transformations and explores the BRST cohomology in different formulations, advancing understanding of Yang-Mills as a BF theory deformation.

Findings

Identified the trivial sector of BRST cohomology for both formulations.

Established groundwork for perturbative calculations in BF-Yang-Mills theory.

Clarified the relationship between standard and extended formulations.

Abstract

We study the most general renormalization transformations for the first-order formulation of the Yang-Mills theory. We analyze, in particular, the trivial sector of the BRST cohomology of two possible formulations of the model: the standard one and the extended one. The latter is a promising starting point for the interpretation of the Yang-Mills theory as a deformation of the topological BF theory. This work is a necessary preliminary step towards any perturbative calculation, and completes some recently obtained results.