A toolkit for ortho-symplectic dualities

Abstract

We propose new confining dualities in $3d$ $\mathcal{N}\!=\!2$ gauge theories with orthogonal gauge groups, with and without monopole superpotentials. Deriving some of those dualities requires a sequence of gauging and Higgsing for a $\mathbb{Z}_2$ symmetry. This prevents the gauge theory from developing a smooth quantum moduli space and affects the global structure of the gauge group, muting it from $SO$ to $O_+$ . The confining dualities provide tools to deconfine fields transforming in the symmetric rank-$2$ representation of classical gauge groups. As an application, we propose and derive S-confining dualities for $SO(N)$ $(Sp(N))$ gauge theories with an adjoint and $1$ $(2)$ fundamentals, respectively. From these S-confining dualities, we readily obtain various duality appetizers and the $3d$ mirror of $A_{2N}$ Argyres-Douglas theories.