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.

1+33 pages, 5 eps figures; v2: references added, some notational changes and minor corrections

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Cited by in corpus (11)

• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Matrix Models and D-branes in Twistor String Theory
• Time-Space Noncommutative Abelian Solitons
• Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
• Noncommutative Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
• Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
• Noncommutative Solitons
• Solitons of Sigma Model on Noncommutative Space as Solitons of Electron System
• Exact BPS bound for noncommutative baby Skyrmions
• Noncommutative Q-Lumps