Algebraic renormalization of the BF Yang-Mills Theory

TL;DR

This paper demonstrates the quantum equivalence of Yang-Mills theory and its first order BF formulation, introducing an auxiliary vector field to interpret it as a perturbation of a topological BF model.

Contribution

It establishes all-order perturbative equivalence between Yang-Mills and a BF-based formulation, using algebraic renormalization and auxiliary fields.

Findings

Yang-Mills theory is quantum equivalent to its BF formulation.

Introduction of a nonphysical vector field aids in interpretation as a BF perturbation.

The equivalence holds to all orders in perturbation theory.

Abstract

We discuss the quantum equivalence, to all orders of perturbation theory, between the Yang-Mills theory and its first order formulation through a second rank antisymmetric tensor field. Moreover, the introduction of an additional nonphysical vector field allows us to interpret the Yang-Mills theory as a kind of perturbation of the topological BF model.