3d dualities from 4d dualities for orthogonal groups

TL;DR

This paper explores how 4d supersymmetric dualities for orthogonal gauge groups translate into 3d dualities, revealing new relationships and verifying them through index computations.

Contribution

It extends 4d-3d duality relations to orthogonal groups, including Chern-Simons terms, and clarifies the dualities between different O(N) theories in 3d.

Findings

Derived 3d dualities from 4d dualities for orthogonal groups.

Established dualities involving O(N)_ ext{±} and Spin(N) theories.

Verified dualities using index computations.

Abstract

We extend recent work on the relation of 4d and 3d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO(N) gauge theories in 4d plays an important role in this relation. We show that the 4d duality leads to a 3d duality between an SO(N_c) gauge theory with N_f flavors and an SO(N_f-N_c+2) theory with N_f flavors and extra singlets, and we derive its generalization in the presence of Chern-Simons terms. There are two different O(N) theories in 3d, which we denote by O(N)_\pm, and we also show that the O(N_c)_- gauge theory is dual to a Spin(N_f-N_c+2) theory, and derive from 4d the known duality between O(N_c)_+ and O(N_f-N_c+2)_+. We verify the consistency of these 3d dualities by various methods, including index computations.