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

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.