Noncommutative solitons on Kahler manifolds

TL;DR

This paper develops a new framework for constructing and analyzing scalar noncommutative multi-solitons on Kahler manifolds using Berezin's geometric quantization, revealing stability conditions and interaction behaviors based on curvature.

Contribution

It introduces a novel method for creating noncommutative solitons on Kahler manifolds via deformation quantization and characterizes their stability and interactions on various symmetric spaces.

Findings

Stable solitons are expressed as generalized coherent states on homogeneous Kahler manifolds.

On positively curved manifolds, solitons attract; on negatively curved, they repel.

The formalism applies to spheres, hyperbolic planes, tori, and symmetric bounded domains.

Abstract

We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kahler manifold by using Berezin's geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/hbar correction to the soliton energy and for homogeneous Kahler manifolds obtain that the stable solitons are given in terms of generalized coherent states. We apply this general formalism to a number of examples, which include the sphere, hyperbolic plane, torus and general symmetric bounded domains. As a general feature we notice that on homogeneous manifolds of positive curvature, solitons tend to attract each other, while if the curvature is negative they will repel each other. Applications of these results are discussed.