Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability

TL;DR

This paper explores noncommutative solitons, deriving solutions at infinite theta, analyzing stability, and examining finite theta effects, including quantization and bound states, revealing new insights into their dynamics and interactions.

Contribution

It provides the first explicit N-soliton solutions at infinite theta and incorporates finite theta corrections, advancing understanding of soliton stability and quantized bound states.

Findings

N-soliton solutions at infinite theta derived

Finite theta corrections induce short-range attraction

Quantization reveals s-wave bound states

Abstract

We find the N-soliton solution at infinite theta, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading 1/theta corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite theta corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite theta, we find an s-wave bound state.