Six Easy Pieces: interplays among dualities in 4d, 3d and 2d

TL;DR

This paper explores dualities in 4d, 3d, and 2d gauge theories, revealing new phases and relationships through tensor deconfinement and partition function analysis, including novel dualities involving special unitary and symplectic groups.

Contribution

It introduces new dualities and phases in lower-dimensional gauge theories derived from 4d models using tensor deconfinement and partition function techniques.

Findings

Identification of a mixed IR phase with Coulomb and free magnetic components.

Derivation of dualities between SU, SO, and symplectic gauge theories in 3d and 2d.

Proposal of new dualities in 2d between special unitary and symplectic theories.

Abstract

In this paper we consider 4d $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an interacting non-Abelian Coulomb phase and a free magnetic phase. Through tensor deconfinement, we show that baryonic deformations lead to a non-Abelian free magnetic phase. Along the analysis we obtain a duality with symplectic SQCD that can be further reduced to 3d and 2d. In the 3d case the analysis of the three sphere partition function allows one to obtain dualities between $\mathrm{SU}(N)$ with a two index symmetric tensor and $\mathrm{SO}(N)$ theories. On the other hand, in 2d we recover dualities already known in the literature and propose new ones between special unitary and symplectic gauge theories.