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 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.