Evidence for Aharony duality for orthogonal gauge groups
Chiung Hwang, Kyung-Jae Park, Jaemo Park
TL;DR
The paper addresses the extension of Aharony duality to 3d $\mathcal{N}=2$ theories with orthogonal gauge groups and vector matter. It employs exact tools—$S^3$ partition functions from localization and the 3d superconformal index—to test the duality between the electric $O(N_c)$ theory with $N_f$ flavors and the magnetic $O(N_f-N_c+2)$ theory with singlets $M^{\{ab\}}$ and $Y$, coupled by $W=M^{\{ab\}}q^i_a q^i_b+Yy$. The results show precise agreement of partition functions as a function of the IR $R$-charge $\Delta_Q$ (determined by $Z$-minimization) and perfect matching of the superconformal indices, including careful treatment of the $Z_2$ projection and chiral ring structures; exceptional cases are analyzed via operator counting and cancellations. These findings extend known dualities to orthogonal groups, clarify the role of monopole operators in the duality, and propose ADS-like superpotential terms in certain magnetic theories, offering a robust framework for Seiberg-like dualities in 3d CS-matter systems.
Abstract
We study the Aharony duality for three dimensional $\mathcal N=2$ supersymmetric gauge theories for orthogonal gauge groups with matters in vector representation. We provide the evidence for the duality by working out the partition function on $S^3$ and the superconformal index, which show perfect agreement.