The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4

TL;DR

This paper demonstrates that U(1) Yang-Mills theory on noncommutative R^4 is renormalizable at one-loop, with an asymptotically free beta function, and the noncommutative structure remains unrenormalized at this level.

Contribution

It provides the first one-loop renormalization analysis of U(1) Yang-Mills on noncommutative R^4, including the computation of the beta function and the non-renormalization of the Weyl-Moyal matrix.

Findings

The theory is renormalizable at one-loop.

The beta function indicates asymptotic freedom.

The noncommutative structure is not renormalized at one-loop.

Abstract

We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.