Novel Spin and Statistical Properties of Nonabelian Vortices

TL;DR

This paper investigates the unique statistical and spin properties of nonabelian vortices in 2+1D gauge theories, revealing novel quantum states, Fermi statistics, and fractional behaviors, with implications for cosmic strings in 3+1D.

Contribution

It introduces new models demonstrating nonabelian vortex statistics, including Fermi behavior and fractional properties, expanding understanding of topological quantum states.

Findings

Vortices can transform symmetric states into antisymmetric ones via flux interactions.

Existence of vortex states obeying Fermi statistics.

Vortices can exhibit fractional 'Cheshire spin' and other fractional behaviors.

Abstract

We study the statistics of vortices which appear in (2+1)--dimensional spontaneously broken gauge theories, where a compact group G breaks to a finite nonabelian subgroup H. Two simple models are presented. In the first, a quantum state which is symmetric under the interchange of a pair of indistinguishable vortices can be transformed into an antisymmetric state after the passage through the system of a third vortex with an appropriate $H$-flux element. Further, there exist states containing two indistinguishable spinless vortices which obey Fermi statistics. These results generalize to loops of nonabelian cosmic string in 3+1 dimensions. In the second model, fractional analogues of the above behaviors occur. Also, composites of vortices in this theory may possess fractional ``Cheshire spin'' which can be changed by passing an additional vortex through the system.