Novel spin and statistical properties of nonabelian vortices

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 intercharge of a pair of indistinguishable vortices can be transformed into an antisymmetric state after the passage through the system of the third vortex with an appropriate H-flux element. Further, there exist states containing two indistinguishable spinless vortices which obey Fermi statistics. In the second model, fractional analogues of the above behaviors occur. Also, composites of vortices in this theory may posses fractional “Cheshire spin” which can be changed by passing an additional vortex through the system.