Seiberg-like duality in three dimensions for orthogonal gauge groups

TL;DR

This paper proposes a Seiberg-like duality for 3d ${\mathcal{N}}=2$ Chern-Simons theories with orthogonal gauge groups and vector matter, mapping $O(N_c)_k$ to $O(N_f+|k|+2-N_c)_{-k}$ with a magnetic sector containing a symmetric meson $M^{ij}$ and quarks $q_i$ and superpotential $W=\sqrt{2} q_i q_j M^{ij}$. It relates this duality to orthogonal level-rank duality and Aharony dualities, and extends to a ${\mathcal{N}}=3$ version to clarify the duality structure. The main contribution is a detailed numerical check via exact $S^3$ partition functions computed by localization, together with $Z$-extremization to determine conformal dimensions, demonstrating strong evidence for the duality across small-rank examples. The results illustrate how 3d dualities with orthogonal groups interpolate between level-rank dualities and 4d Seiberg-like dualities, and establish a concrete operator map and computational framework for future analytic proofs.

Abstract

We propose a duality for N=2 d=3 Chern-Simons gauge theories with orthogonal gauge groups and matter in the vector representation. This duality generalizes level-rank duality for pure Chern-Simons gauge theories with orthogonal gauge groups and is reminiscent of Seiberg duality in four dimensions. We perform extensive checks by comparing partition functions of theories related by dualities. We also determine the conformal dimensions of fields using Z-extremization.