The noncommutative U(1) Higgs-Kibble model in the enveloping-algebra formalism and its renormalizability

TL;DR

This paper investigates the renormalizability of the noncommutative U(1) Higgs-Kibble model using the enveloping-algebra formalism, revealing one-loop renormalizability in the gauge sector but non-renormalizability in the matter sector.

Contribution

It demonstrates the gauge sector's one-loop renormalizability at first order in theta^{mu nu} within the enveloping-algebra approach, suggesting a possible new symmetry.

Findings

Gauge sector is one-loop renormalizable at first order in theta^{mu nu}.

Matter sector remains non-renormalizable regardless of the phase.

Potential existence of a new symmetry in the gauge sector.

Abstract

We discuss the renormalizability of the noncommutative U(1)Higgs-Kibble model formulated within the enveloping-algebra approach. We consider both the phase of the model with unbroken gauge symmetry and the phase with spontaneously broken gauge symmetry. We show that against all odds the gauge sector of the model is always one-loop renormalizable at first order in theta^{mu nu}, perhaps, hinting at the existence of a new symmetry of the gauge sector of the model. However, we also show that the matter sector of the model is non-renormalizable whatever the phase.