Non-Abelian statistics versus the Witten anomaly

Abstract

This paper is motivated by prospects for non-Abelian statistics of deconfined particlelike objects in $3+1$ dimensions, realized as solitons with localized Majorana zero modes. 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 zero mode 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.