Vortex Zero Modes, Large Flux Limit and Ambjørn-Nielsen-Olesen Magnetic Instabilities

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 Ambjørn. 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.

arXiv comment22 pages, 10 figures

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• NonAbelian Vortices, Large Winding Limits and Aharonov-Bohm Effects
• Small Winding-Number Expansion: Vortex Solutions at Critical Coupling
• Nonlinear Problems Inspired by the Born--Infeld Theory of Electrodynamics
• Zero Modes of Fermions Trapped by Giant Vortices
• Dyonic non-Abelian vortex strings in supersymmetric and non-supersymmetric theories: tensions and higher derivative corrections