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

Abstract

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.

17 pages, typos corrected, ref. added

References in corpus (2)

• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Monopole Operators and Mirror Symmetry in Three Dimensions

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