Non-Abelian statistics versus the Witten anomaly

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.