The Moduli Space of Noncommutative Vortices

TL;DR

This paper studies the moduli space of noncommutative vortices in the abelian Higgs model, providing a perturbative solution to the Bogomoln'yi equations and explicit metrics in the large noncommutativity limit.

Contribution

It introduces a perturbative approach to solve the Bogomoln'yi equations for noncommutative vortices and derives explicit moduli space metrics in the large noncommutativity limit.

Findings

Perturbative solutions to Bogomoln'yi equations are obtained to all orders.

The moduli space metric reduces to the trace of a k-dimensional matrix.

Explicit metric expression is provided in the large noncommutativity limit.

Abstract

The abelian Higgs model on the noncommutative plane admits both BPS vortices and non-BPS fluxons. After reviewing the properties of these solitons, we discuss several new aspects of the former. We solve the Bogomoln'yi equations perturbatively, to all orders in the inverse noncommutivity parameter, and show that the metric on the moduli space of k vortices reduces to the computation of the trace of a k-dimensional matrix. In the limit of large noncommutivity, we present an explicit expression for this metric.