Vortex Zero Modes, Large Flux Limit and Ambj{\o}rn-Nielsen-Olesen Magnetic Instabilities

TL;DR

This paper explores the relationship between vortex zero modes and magnetic instabilities in non-Abelian vortices, revealing how large flux limits and background magnetic fields influence zero mode spectra and moduli space dimensions.

Contribution

It provides a unified analysis of zero modes in vortex configurations and their connection to magnetic instabilities, extending previous results to non-Abelian cases and large flux limits.

Findings

Zero modes are correctly counted in large flux vortex configurations.

BPS vortices mark the onset of magnetic instabilities.

The dimension of the moduli space matches predictions from instability analysis.

Abstract

In the large flux limit vortices become flux tubes with almost constant magnetic field in the interior region. This occurs in the case of non-Abelian vortices as well, and the study of such configurations allows us to reveal a close relationship between vortex zero modes and the gyromagnetic instabilities of vector bosons in a strong background magnetic field discovered by Nielsen, Olesen and Ambj{\o}rn. The BPS vortices are exactly at the onset of this instability, and the dimension of their moduli space is precisely reproduced in this way. We present a unifying picture in which, through the study of the linear spectrum of scalars, fermions and W bosons in the magnetic field background, the expected number of translational, orientational, fermionic as well as semilocal zero modes is correctly reproduced in all cases.