A - BCD dualities

Abstract: In this paper we propose 4d and 3d dualities among special unitary gauge theories with fundamentals and antisymmetric flavors and symplectic or orthogonal gauge theories with fundamentals and two index tensor matter. The various dualities originate from a conjectured 4d self-duality for $SU(N)$ with an antisymmetric and four fundamental flavors. While we provide a proof of such self duality for $SU(4)$, we focus on baryonic deformations for the cases at higher ranks. The deformations give rise to RG flows, deforming the self duality into new types of dualities, involving $SU(N)$ and $USp(2M)$ gauge theories, where the precise value of $M$ depends on the baryonic deformation. We provide strong checks on the validity of these dualities, by proving the integral identities among their superconformal index. By dimensional reduction on a circle, real mass flows and other deformations we then find a rich set of new dualities in 3d. These dualities are first conjectured from localization, by the application of the duplication formula for the one loop determinants of the matter fields, and then they are proved by using the tensor deconfinement technique.