Perturbative BF-Yang-Mills theory on noncommutative R^4

TL;DR

This paper formulates a U(1) BF-Yang-Mills theory on noncommutative R^4, demonstrating its asymptotic freedom and analyzing its one-loop renormalization properties, revealing similarities to commutative SU(N) theories.

Contribution

It introduces a noncommutative U(1) BF-Yang-Mills theory as a deformation of pure BF theory and studies its quantization and renormalization.

Findings

The theory is asymptotically free.

One-loop beta function matches that of SU(N) Yang-Mills.

Renormalization properties are consistent with known gauge theories.

Abstract

A U(1) BF-Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is presented and in this formulation the U(1) Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is seen as a deformation of the pure BF theory. Quantization using BRST symmetry formalism is discussed and Feynman rules are given. Computations at one-loop order have been performed and their renormalization studied. It is shown that the U(1) BFYM on noncommutative ${\mathbb{R}}^4$ is asymptotically free and its UV-behaviour in the computation of the $\beta$-function is like the usual SU(N) commutative BFYM and Yang Mills theories.