Cohomology and Renormalization of BFYM Theory in three Dimensions

TL;DR

This paper explores two formulations of 3D Yang-Mills theory as deformations of BF theory, analyzing their cohomology, renormalization, and stability, demonstrating they are anomaly-free and well-behaved under quantum corrections.

Contribution

It introduces and compares two first order formulations of 3D Yang-Mills theory as BF deformations, with detailed cohomological and renormalization analysis.

Findings

Both models are anomaly free.

Theories are stable under radiative corrections.

Counterterms involve complex matricial renormalization.

Abstract

The first order formalism for 3D Yang-Mills theory is considered and two different formulations are introduced, in which the gauge theory appears to be a deformation of the topological BF theory. We perform the quantization and the algebraic analysis of cohomology and renormalization for both the models, which are found to be anomaly free. We discuss also their stability against radiative corrections, giving the full structure of possible counterterms, requiring an involved matricial renormalization of fields and sources.