On a gauge action on sigma model solitons

TL;DR

This paper explores gauge actions on sigma model solitons over noncommutative tori, introducing new solitons from Gabor frames and analyzing how to gauge a Gaussian to a specific Gabor frame.

Contribution

It introduces new classes of solitons derived from Gabor frames and studies gauge conditions on Gaussian functions within noncommutative geometry.

Findings

Quantified conditions for gauging a Gaussian to a prescribed Gabor frame

Developed new classes of solitons using Gabor frames

Extended understanding of gauge actions in noncommutative sigma models

Abstract

In this paper we consider a gauge action on sigma model solitons over noncommutative tori as source spaces, with a target space made of two points introduced in \cite{DKL:Sigma}. Using new classes of solitons from Gabor frames, we quantify the condition about how to gauge a Gaussian to a prescribed Gabor frame.