A note on BPS vortex bound states

A Alonso-Izquierdo,W Garcia Fuertes,J Mateos Guilarte

doi:10.1016/j.physletb.2015.11.070

A Alonso-Izquierdo, W Garcia Fuertes + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2015.11.070

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Abstract

In this note we investigate bound states, where scalar and vector bosons are trapped by BPS vortices in the Abelian Higgs model with a critical ratio of the couplings. A class of internal modes of fluctuation around cylindrically symmetric BPS vortices is characterized mathematically, analyzing the spectrum of the second-order fluctuation operator when the Higgs and vector boson masses are equal. A few of these bound states with low values of quantized magnetic flux are described fully, and their main properties are discussed.

Highlights

Very soon after the discovery of Abrikosov quantized flux lines in the Ginzburg-Landau theory of Type II superconductors [1], the existence and nature of fermionic bound states on these vortex filaments were discussed by de Gennes et al in Reference [2]
Quantized magnetic flux lines were rediscovered by Nielsen and Olesen in the Abelian Higgs model, see [3], a finding that enhanced the interest of these topological defects by promoting them to the relativistic and quantum world
By adjusting the couplings in the Abelian Higgs model to drive the system to the critical point between Type II and Type I superconductors, Bogomolny showed, see [4], that quantized vortex lines still exist but move without interaction with respect to each other

Summary

Introduction

Very soon after the discovery of Abrikosov quantized flux lines in the Ginzburg-Landau theory of Type II superconductors [1], the existence and nature of fermionic bound states on these vortex filaments were discussed by de Gennes et al in Reference [2]. Bosonic vortex bound states were investigated by Goodman and Hindmarsh, see [5], in the context of the Abelian Higgs model for any value of the parameter governing the transition between Type I and Type II superconductivity. In this short note we shall focus on finding BPS vortex bound states and we shall describe these internal boson-vortex modes by a mixture of analytical and numerical methods, at least at the same level of numerical precision as the BPS vortex solutions themselves

BPS vortex fluctuations

Spectrum of cylindrically symmetric BPS vortex fluctuations

Positive eigenvalue bound states of the small vortex fluctuation operator