The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level

TL;DR

This paper demonstrates that noncommutative U(N) Yang-Mills theory can be consistently renormalized at one-loop level while preserving BRS invariance, ensuring gauge symmetry is maintained after quantum corrections.

Contribution

It establishes the one-loop renormalizability of noncommutative U(N) Yang-Mills theory in a BRS invariant manner, including explicit calculations of divergences.

Findings

Successful multiplicative renormalization of coupling, fields, and gauge parameter.

Validation of Slavnov-Taylor, gauge-fixing, and ghost equations at one-loop.

Explicit determination of UV divergent parts of 1PI diagrams.

Abstract

We show that U(N) Yang-Mills theory on noncommutative Minkowski space-time can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov-Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order $\hbar$, for the MS renormalized noncommutative U(N) Yang-Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.