A note on local BRST cohomology of Yang-Mills type theories with free abelian factors

TL;DR

This paper extends the analysis of local BRST cohomology in Yang-Mills theories to include models with free abelian factors, providing insights into gauge anomalies, deformations, and counterterms.

Contribution

It generalizes previous cohomology computations to theories with free abelian factors, clarifying the role of dynamics and offering explicit solutions for specific models.

Findings

Cohomology structure influenced by free abelian factors

Implications for gauge anomalies and consistent deformations

Explicit solutions in certain models

Abstract

We extend previous work on antifield dependent local BRST cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.