The Higgs mechanism in non-commutative gauge theories

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.

Noncommutative field theory

“…It has also been argued that spontaneously broken noncommutative gauge theories are renormalizable (Petriello, 2001).…”

Instability of non-commutative SYM theories at finite temperature

“…Let us remind that in ordinary gauge theories at zero temperature, the poles of propagators are gauge invariant quantities [26]. In non-commutative gauge theories, there is no general proof of this statement, but only checks at one-loop order [5] [27] 3 .…”

Vacuum configurations for renormalizable non-commutative scalar models

“…Other investigations regarding different non-commutative models were done in [28,29,30,31]. Within these models it was found that the situation for the Goldstone theorem, followed rather closely the features of the commutative case.…”