Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons

TL;DR

This paper explores the dynamics of noncommutative sigma-model solitons, revealing that the traditional moduli-space approximation may not accurately describe two-soliton interactions, thus challenging existing adiabatic methods.

Contribution

It establishes a connection between noncommutative sigma-model solitons and scalar-field solitons, and analyzes the limitations of moduli-space approximation in this context.

Findings

Moduli-space dynamics are unaffected by WZW-like terms.

Exact two-soliton configurations do not match moduli-space predictions.

Challenges the validity of adiabatic approximation for noncommutative solitons.

Abstract

In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space C^k/S_k features a natural K"ahler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.