One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case

TL;DR

This paper investigates the one-loop renormalizability of a spontaneously broken U(1) x U(1) gauge theory on noncommutative spacetime, demonstrating that all divergences can be consistently renormalized.

Contribution

It provides the first complete one-loop analysis showing the renormalizability of a noncommutative gauge theory with spontaneous symmetry breaking and product gauge groups.

Findings

All ultraviolet divergences are removable with a finite set of renormalization constants.

Gauge interactions maintain their structure at one loop despite noncommutativity.

The model remains consistent with gauge symmetry after renormalization.

Abstract

A generalization of the standard electroweak model to noncommutative spacetime would involve a product gauge group which is spontaneously broken. Gauge interactions in terms of physical gauge bosons are canonical with respect to massless gauge bosons as required by the exact gauge symmetry, but not so with respect to massive ones; and furthermore they are generally asymmetric in the two sets of gauge bosons. On noncommutative spacetime this already occurs for the simplest model of U(1) x U(1). We examine whether the above feature in gauge interactions can be perturbatively maintained in this model. We show by a complete one loop analysis that all ultraviolet divergences are removable with a few renormalization constants in a way consistent with the above structure.