Non-abelian vortices and non-abelian statistics

TL;DR

This paper explores the unique interactions of non-abelian vortices in two dimensions, highlighting how quantum effects like the Aharonov-Bohm phenomenon lead to unconventional scattering behaviors and indistinguishability.

Contribution

It introduces a detailed analysis of non-abelian vortex interactions, emphasizing the role of quantum number exchange and multi-valued scattering cross sections.

Findings

Vortex interactions exhibit multi-valued scattering cross sections.

Quantum number exchange can occur even between vortices with different quantum states.

Vortices can be indistinguishable despite having distinct quantum numbers.

Abstract

We study the interactions of non-abelian vortices in two spatial dimensions. These interactions have novel features, because the Aharonov-Bohm effect enables a pair of vortices to exchange quantum numbers. The cross section for vortex-vortex scattering is typically a multi-valued function of the scattering angle. There can be an exchange contribution to the vortex-vortex scattering amplitude that adds coherently with the direct amplitude, even if the two vortices have distinct quantum numbers. Thus two vortices can be ``indistinguishable'' even though they are not the same.