Anyons, ’t Hooft loops and a Generalized Connection in Three Dimensions

We consider a generalized connection in three dimensions and show that it emerges in Chern-Simons-Maxwell theories when one studies the disorder instanton operator. We generalized this construction to non-Abelian theories and find that the disorder operator (the ’t Hooft operator) is equivalent to a generalized Wilson loop in a representation that depends on the Chern-Simons term. We speculate about the effective action of the disorder operator and its application to the possible phases of the theory at the infra-red. We also show that fractional statistics can emerge in gauge theories without a Chern-Simons term if the generalized connection rather than the ordinary connection is used to couple charge particles.