Sigma-Model Solitons in the Noncommutative Plane: Construction and Stability Analysis

TL;DR

This paper explores noncommutative sigma model solitons in two dimensions, analyzing their construction, moduli spaces, and stability, revealing unstable modes in U(n) models but stability in Grassmannian models.

Contribution

It provides a unified construction of abelian and nonabelian noncommutative solitons and analyzes their stability properties.

Findings

Unstable mode found in U(n) models

Stable configurations identified in Grassmannian models

Explicit spectrum of the Hessian for diagonal multi-solitons

Abstract

Noncommutative multi-solitons are investigated in Euclidean two-dimensional U(n) and Grassmannian sigma models, using the auxiliary Fock-space formalism. Their construction and moduli spaces are reviewed in some detail, unifying abelian and nonabelian configurations. The analysis of linear perturbations around these backgrounds reveals an unstable mode for the U(n) models but shows stability for the Grassmannian case. For multi-solitons which are diagonal in the Fock-space basis we explicitly evaluate the spectrum of the Hessian and identify all zero modes. It is very suggestive but remains to be proven that our results qualitatively extend to the entire multi-soliton moduli space.