  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 generalize 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
applications to the possible phases of the theory in 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 charged particles.
