Noncommutative scalar solitons: existence and nonexistence

TL;DR

This paper investigates the existence of scalar solitons in noncommutative field theories, establishing conditions under which such solutions exist or do not exist based on the noncommutativity parameter.

Contribution

It provides rigorous proofs for the existence of spherically symmetric solitons at large noncommutativity and their absence at small noncommutativity.

Findings

Existence of spherically symmetric solutions for large 

Nonexistence of solutions for small 

Results depend on the size of the noncommutativity parameter 

Abstract

We study the variational equations for solitons in noncommutative scalar field theories in an even number of spatial dimensions. We prove the existence of spherically symmetric solutions for a sufficiently large noncommutativity parameter $\theta$ and we prove the absence of spherically symmetric solutions for small $\theta$.