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

TL;DR

This paper explores a generalized connection in three-dimensional gauge theories, linking it to 't Hooft operators, Wilson loops, and fractional statistics, with implications for understanding phases in these theories.

Contribution

It introduces a generalized connection framework in 3D gauge theories, connecting disorder operators to Wilson loops and fractional statistics without Chern-Simons terms.

Findings

Disorder operators are equivalent to generalized Wilson loops.

Fractional statistics can emerge without Chern-Simons terms.

Generalized connection influences the effective action and phases of the theory.

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.