Travelling waves in multivortex configurations

TL;DR

This paper studies traveling wave zero modes in multivortex configurations within the Abelian Higgs model, revealing their independence from vortex separation and constructing a string description, with insights into modes outside the Bogomol'nyi limit.

Contribution

It introduces a detailed analysis of zero modes as traveling waves in multivortex solutions and provides a string-theoretic interpretation, extending understanding beyond the Bogomol'nyi limit.

Findings

Zero modes are traveling waves with light speed along vortices.

Zero modes are independent of vortex mutual separations.

String description of zero modes is constructed.

Abstract

We investigate zero modes of a multivortex background which are due to the energetic degeneracy of the planar static n-vortex solution in Bogomol'nyi limit of the Abelian Higgs model parametrised by a set of 2n real parameters. The zero modes take the form of waves travelling with a speed of light independently along each of the vortices irrespectively to their mutual separations. String description of these zero modes is constructed. We also comment on the remnants of the modes a little outside of the Bogomol'nyi limit.