A note on BPS vortex bound states

TL;DR

This paper studies bound states of scalar and vector bosons trapped by BPS vortices in the Abelian Higgs model, analyzing fluctuation spectra and identifying specific low-flux bound states.

Contribution

It characterizes a class of internal fluctuation modes around BPS vortices and describes some low-flux bound states in detail.

Findings

Identified bound states with low magnetic flux.

Analyzed the spectrum of fluctuations around BPS vortices.

Discussed properties of specific bound states.

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, analysing 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.