Monopole operators in three-dimensional N=4 SYM and mirror symmetry

TL;DR

This work analyzes non-abelian monopole operators in the IR of three-dimensional gauge theories, using a large $N_f$ expansion and the operator-state correspondence to construct (anti-)chiral monopole primaries and compute their global quantum numbers. Focusing on SU($N_c$) with fermionic matter and on ${ cal N}=4$ SU(2) with hypermultiplets, the authors derive monopole spectra via radial quantization in monopole backgrounds and verify that the resulting charges align with three-dimensional mirror symmetry predictions. For the ${ cal N}=4$ SU(2) case, the dual twisted theory is identified and the mapping between monopole operators and dual chiral primaries is established, including the identification $w o z$ and the unique $( ext{anti-})chiral primaries corresponding to the $x$ and $y$ operators. The findings provide a nonperturbative check of 3d mirror symmetry in a non-Abelian setting and illustrate how integral R-charges protect the exactness of these quantum numbers in the large $N_f$ limit. The methods and results point toward generalizations to larger gauge groups and enrich the understanding of Coulomb/Higgs branch dualities in three dimensions.

Abstract

We study non-abelian monopole operators in the infrared limit of three-dimensional SU(N_c) and N=4 SU(2) gauge theories. Using large N_f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators which are (anti-)chiral primaries and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified.