Noncommutative Vortices and Instantons from Generalized Bose Operators

TL;DR

This paper introduces a novel approach using generalized Bose operators to construct topologically non-trivial solutions like vortices and instantons in noncommutative gauge theories, revealing new instanton solutions and relations between topological charge and representation structure.

Contribution

It presents a new method leveraging generalized Bose operators for constructing noncommutative vortices and instantons, establishing a link between topological charge and reducible representations.

Findings

New relation between topological charge and representation multiplicity

Construction of noncommutative vortices and instantons using generalized Bose operators

Discovery of instantons not unitarily equivalent to known solutions

Abstract

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.