Low-Energy Dynamics of Noncommutative CP^1 Solitons in 2+1 Dimensions

TL;DR

This paper studies the low-energy behavior of solitons in a noncommutative CP^1 model in 2+1 dimensions, revealing that single soliton dynamics match the commutative case and singularities in two-soliton space are smoothed out.

Contribution

It demonstrates that noncommutativity removes singularities in the two-soliton moduli space and ensures a smooth commutative limit, advancing understanding of soliton dynamics in noncommutative field theories.

Findings

Single soliton dynamics are unchanged by noncommutativity.

Singularity in the two-soliton moduli space disappears in the noncommutative model.

Two-soliton metric has a smooth limit as noncommutativity vanishes.

Abstract

We investigate the low-energy dynamics of the BPS solitons of the noncommutative CP^1 model in 2+1 dimensions using the moduli space metric of the BPS solitons. We show that the dynamics of a single soliton coincides with that in the commutative model. We find that the singularity in the two-soliton moduli space, which exists in the commutative CP^1 model, disappears in the noncommutative model.We also show that the two-soliton metric has the smooth commutative limit.