The CP(n) Model on Noncommutative Plane

TL;DR

This paper constructs a noncommutative CP(n) model with self-dual solitons, demonstrating energy bounds, topological charge quantization, and discussing implications for noncommutative Yang-Mills instantons.

Contribution

It introduces a consistent noncommutative CP(n) model with solitons saturating the Bogomolny bound and explores their properties and implications.

Findings

Self-dual solitons saturate the energy bound.

Topological charge is quantized as an integer.

Solutions are regular everywhere.

Abstract

We construct the consistent CP(n) model on noncommutative plane. The Bogomolny bound on the energy is saturated by (anti-)self-dual solitons with integer topological charge, which is independent of their scaling and orientation. This integer quantization is satisfied for our general solutions, which turns out regular everywhere. We discuss the possible implication of our result to the instanton physics in Yang-Mills theories on noncommutative R^4.