The Higgs Mechanism in Non-commutative Gauge Theories

TL;DR

This paper demonstrates that the non-commutative Abelian Higgs model remains one-loop renormalizable with preserved BRST invariance, providing detailed calculations of beta functions and showing gauge independence of physical parameters.

Contribution

It establishes one-loop renormalizability of the non-commutative Abelian Higgs model and the broken O(2) sigma model, with explicit beta functions and gauge independence results.

Findings

BRST invariance is maintained at one loop.

The theory is one-loop renormalizable.

Physical couplings and masses are gauge independent.

Abstract

This paper investigates the non-commutative version of the Abelian Higgs model at the one loop level. We find that the BRST invariance of the theory is maintained at this order in perturbation theory, rendering the theory one-loop renormalizable. Upon removing the gauge field from the theory we also obtain a consistent continuum renormalization of the broken O(2) linear sigma model, contradicting results found in the literature. The beta functions for the various couplings of the gauged U(1) theory are presented, as are the divergent contributions to every one particle irreducible (1PI) function. We find that all physical couplings and masses are gauge independent. A brief discussion concerning the symmetries $P$, $C$, and $T$ in this theory is also given.