Gauge theory solitons on noncommutative cylinder

TL;DR

This paper extends solution generation methods for gauge theory solitons to noncommutative cylinders, constructing explicit solutions and analyzing their perturbations, thus broadening the understanding of noncommutative gauge theories.

Contribution

It introduces a novel approach to generate gauge theory solitons on noncommutative cylinders using partial isometries and projectors, generalizing previous methods from noncommutative planes.

Findings

Constructed explicit gauge theory solitons on noncommutative cylinders.

Developed a framework of partial isometries and projectors for the algebra.

Analyzed the spectrum of perturbations around the solitons.

Abstract

We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors in the algebra of the cylinder, and an isomorphism between the free module and its direct sum with the Fock module on the cylinder. We construct explicitly the gauge theory soliton and evaluate the spectrum of perturbations about this soliton.