Sequential deconfinement and self-dualities in $4d$ $\mathcal{N}\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1$ gauge theories

We apply the technique of sequential deconfinement to the four dimensional $\mathcal{N}\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1$ $Usp(2N)$ 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 $3d$ $\mathcal{N}\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}2$ theories, recovering known fully deconfined duals of $Usp(2N)$ and $U(N)$ gauge theories, and obtaining new ones.