The Moduli Space of Noncommutative Vortices

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.

Invited contribution to special issue of J.Math.Phys. on "Integrability, Topological Solitons and Beyond"; 10 Pages, 1 Figure. v2: revision of history in introduction

References in corpus (8)

• Noncommutative Field Theory
• NS5-Branes, T-Duality and Worldsheet Instantons
• Komaba Lectures on Noncommutative Solitons and D-Branes
• Asymptotic Interactions of Critically Coupled Vortices
• Noncommutative Vortex Solitons
• Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability
• Nielsen-Olesen vortices in noncommutative space
• The dynamics of vortices on S^2 near the Bradlow limit

Cited by in corpus (10)

• Three lectures on noncommutative field theories
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• Transmogrifying Fuzzy Vortices
• Non BPS noncommutative vortices
• Bogomolny equations for vortices in the noncommutative torus
• Vortex solutions in the noncommutative torus
• Lattice vortices induced by noncommutativity
• Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_2$ Coordinates
• Non Abelian Vortices as Instantons on Noncommutative Discrete Space
• Vortex Scattering and Intercommuting Cosmic Strings on a Noncommutative Spacetime