Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory

TL;DR

This paper investigates the one-loop quantum corrections in non-commutative U(N) Yang-Mills theory, examining its renormalizability, gauge invariance, and the behavior of the beta function, highlighting differences from commutative theories.

Contribution

It provides a detailed one-loop analysis of non-commutative U(N) Yang-Mills theory, emphasizing the role of U(1) interactions and the non-convergence to commutative limits.

Findings

The theory is renormalizable and gauge invariant at one loop.

The SU(N) sector alone is inconsistent without U(1) interactions.

The non-commutative limit does not recover the commutative theory.

Abstract

We study the U(N) non-commutative Yang-Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the theta --> 0 limit of the U(N) theory does not converge to the ordinary SU(N) x U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.