Feynman rules and beta-function for the BF Yang-Mills Theory

TL;DR

This paper derives Feynman rules and computes the beta-function for BF Yang-Mills theory, showing its renormalization structure and confirming expected ultraviolet behavior in a first-order formalism.

Contribution

It provides the Feynman rules and analyzes the renormalization and beta-function for BF Yang-Mills theory at the quantum level, connecting topological and gauge theories.

Findings

Feynman rules for BF-YM theory derived

Renormalization structure analyzed

Beta-function computed and matches expected results

Abstract

Yang-Mills theory in the first order formalism appears as the deformation of a topological field theory, the pure BF theory. We discuss this formulation at the quantum level, giving the Feynman rules of the BF-YM theory, the structure of the renormalization and checking its uv-behaviour in the computation of the beta-function which agrees with the expected result.