Aharony duality and monopole operators in three dimensions

TL;DR

This work tests three-dimensional ${\cal N}=2$ Aharony dualities by computing and matching the superconformal indices of dual pairs with unitary and symplectic gauge groups, explicitly including monopole (GNO) sectors. By analyzing index expansions (and using a fugacity $y$ when IR R-charges are not known) and mapping monopole operators to magnetic composites, the authors verify index equality for several dual pairs and clarify the operator dictionary, including the role of monopole operators in the chiral ring. They argue that the chiral ring is freely generated by mesons $M_i^{\tilde{j}}$ and minimal monopoles $v_{\pm}$, with higher monopoles typically absent or incidental under deformation; GNO charges do not label Hilbert-space sectors. The results extend beyond unitary groups to symplectic theories, where analogous generators and monopole mappings similarly support the dualities. Overall, the paper strengthens nonperturbative checks of Aharony dualities in 3D and clarifies the structure of the chiral ring in these theories, providing a robust framework for sector-by-sector index comparisons and operator matching.

Abstract

We test dualities between three dimensional N = 2 gauge theories proposed by Aharony in [1] by comparing superconformal indices of dual theories. We also extend the discussion of chiral rings matching to include monopole operators.