Monopole Taxonomy in Three-Dimensional Conformal Field Theories

TL;DR

This paper classifies monopole operators in three-dimensional conformal field theories, analyzing their stability and scaling dimensions at infrared fixed points for Abelian and non-Abelian gauge theories with many fermion flavors.

Contribution

It provides a detailed monopole taxonomy, including stability analysis and scaling dimensions, for both Abelian and non-Abelian gauge theories in three dimensions.

Findings

All Abelian monopole backgrounds are stable.

Many non-Abelian backgrounds are stable within each topological class.

Monopole operators transform as non-trivial SU(N_f) representations.

Abstract

We study monopole operators at the infrared fixed points of Abelian and non-Abelian gauge theories with N_f fermion flavors in three dimensions. At large N_f, independent monopole operators can be defined via the state-operator correspondence only for stable monopole backgrounds. In Abelian theories, every monopole background is stable. In the non-Abelian case, we find that many (but not all) backgrounds are stable in each topological class. We calculate the infrared scaling dimensions of the corresponding operators through next-to-leading order in 1/N_f. In the case of U(N_c) QCD with N_f fundamental fermions (and in particular in the QED case, N_c =1), we find that the monopole operators transform as non-trivial irreducible representations of the SU(N_f) flavor symmetry group.