Topological Disorder Operators in Three-Dimensional Conformal Field Theory

TL;DR

This paper introduces monopole operators in 3D conformal field theories, exploring their properties, symmetries, and roles in phases like the Higgs phase, using large N_f expansion techniques.

Contribution

It defines and analyzes a new class of topological disorder operators in 3D CFTs, extending the understanding of their conformal dimensions and symmetry transformations.

Findings

Monopole operators have conformal dimensions of order N_f.

They transform non-trivially under flavor symmetry groups.

Their properties depend on the Chern-Simons coupling.

Abstract

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N_f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.