NonAbelian Vortices, Large Winding Limits and Aharonov-Bohm Effects

TL;DR

This paper explores the behavior of nonAbelian vortices in large winding limits, revealing how gauge couplings influence topological effects like Aharonov-Bohm phenomena and vortex zero modes.

Contribution

It extends the analysis of vortex zero modes and topological effects to more general BPS nonAbelian vortices with gauged symmetries, highlighting the impact of gauge couplings.

Findings

Large winding limit simplifies vortex equations.

Presence of massless gauge fields leads to non-local topological phenomena.

Turning on gauge coupling g_r qualitatively changes the physics.

Abstract

Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used in [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U(1) x SU(N) x SU(N) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N)_{l+r} . The presence of the massless SU(N)_{l+r} gauge fields in 4D bulk introduces all sorts of non-local, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU(N)_r group (g_r=0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant g_r is turned on.