Non-Abelian statistics versus the Witten anomaly

TL;DR

This paper investigates the potential for non-Abelian statistics in 3+1 dimensions through monopole solitons with Majorana zero modes, revealing incompatibility with the Witten anomaly and comparing different realization approaches.

Contribution

It demonstrates that a single Majorana zero mode on monopoles cannot cancel the Witten anomaly, providing new insights into non-Abelian particle statistics in higher dimensions.

Findings

A single Majorana zero mode is incompatible with anomaly cancellation.

Comparison of different models for non-Abelian objects in 3+1 dimensions.

Insights into the limitations of realizing non-Abelian statistics in 3+1D.

Abstract

This paper is motivated by prospects for non-Abelian statistics of deconfined particle-like objects in 3+1 dimensions, realized as solitons with localized Majorana zeromodes. To this end, we study the fermionic collective coordinates of magnetic monopoles in 3+1 dimensional spontaneously-broken SU(2) gauge theories with various spectra of fermions. We argue that a single Majorana zeromode of the monopole is not compatible with cancellation of the Witten SU(2) anomaly. We also compare this approach with other attempts to realize deconfined non-Abelian objects in 3+1 dimensions.