A - BCD dualities

TL;DR

This paper introduces new dualities between 4d and 3d gauge theories with various matter contents, derived from a conjectured self-duality of SU(N) theories, and confirms them through superconformal index identities and tensor deconfinement techniques.

Contribution

It proposes novel 4d and 3d dualities involving special unitary and symplectic gauge theories, extending known self-duality concepts and providing rigorous checks via index identities.

Findings

Proof of self-duality for SU(4)

Derivation of new dualities through baryonic deformations

Validation of dualities via superconformal index identities

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.