Sigma-model solitons on noncommutative spaces

TL;DR

This paper constructs new sigma-model solitons on noncommutative spaces like the Moyal plane and tori using time-frequency analysis, Morita duality, and self-duality equations, revealing their topological properties.

Contribution

It introduces a novel method for constructing sigma-model solitons on noncommutative spaces using Gabor analysis and Morita duality, expanding the understanding of solitons in noncommutative geometry.

Findings

New classes of sigma-model solitons constructed

Solutions exhibit non-trivial topological content

Method connects time-frequency analysis with noncommutative solitons

Abstract

We use results from time-frequency analysis and Gabor analysis to construct new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural action functional leads to self-duality equations for projections in the source algebra. Solutions, having non-trivial topological content, are constructed via suitable Morita duality bimodules.