Scalar Solitons on the Fuzzy Sphere

TL;DR

This paper investigates scalar solitons on the fuzzy sphere, establishing conditions for their existence, constructing stable solutions, and analyzing their properties and stability, with implications for noncommutative geometry.

Contribution

It proves the existence and stability conditions of scalar solitons on the fuzzy sphere and constructs explicit solutions, extending understanding of noncommutative solitons.

Findings

No solitons below a critical radius.

Stable solitons exist above the critical radius.

Multi-lump solutions are unstable.

Abstract

We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. These solutions are rotationally symmetric about an axis and have no allowed deformations. Solitons that describe multiple lumps on the fuzzy sphere can also be constructed but they are not stable.