Sequential deconfinement and self-dualities in $4d$ $\mathcal{N}\!=\!1$ gauge theories

TL;DR

This paper uses sequential deconfinement to analyze 4d $ ext{N}=1$ $Usp(2N)$ gauge theories, proving known self-dualities and discovering new duals upon reduction to 3d, with insights into operator degeneracies.

Contribution

It introduces a sequential deconfinement approach for 4d $ ext{N}=1$ $Usp(2N)$ theories, providing new proofs of self-duality and deriving novel 3d duals.

Findings

Proved the self-duality of $Usp(2N)$ with an antisymmetric and 8 fundamentals.

Identified subtleties in quivers with degenerate operators affecting duality rules.

Derived new 3d duals for $Usp(2N)$ and $U(N)$ gauge theories.

Abstract

We apply the technique of sequential deconfinement to the four dimensional $\mathcal{N}\!=\!1$ $Usp(2N)$ gauge theory with an antisymmetric field and $2F$ fundamentals. The fully deconfined frame is a length-$N$ quiver. We use this deconfined frame to prove the known self-duality of $Usp(2N)$ with an antisymmetric field and $8$ fundamentals. Along the way we encounter a subtlety: in certain quivers with degenerate holomorphic operators, a naive application of Seiberg duality rules leads to an incorrect superpotential or chiral ring. We also consider the reduction to $3d$ $\mathcal{N}\!=\!2$ theories, recovering known fully deconfined duals of $Usp(2N)$ and $U(N)$ gauge theories, and obtaining new ones.