S-confinements from deconfinements

TL;DR

This paper classifies and proves all S-confining dualities for certain 4D $ abla=1$ gauge theories with matter in rank-1 and rank-2 representations, using deconfinement and re-confinement techniques.

Contribution

It provides a complete proof of all S-confining dualities within a specific class, expanding understanding of dualities in supersymmetric gauge theories.

Findings

All S-confining dualities with rank-1 and rank-2 matter are proven.

The classification relies on known dualities for $SU(N)$ and $Usp(2N)$ gauge groups.

Explicit superpotentials are constructed at each step of the proof.

Abstract

We consider four dimensional $\mathcal{N}=1$ gauge theories that are S-confining, that is they are dual to a Wess-Zumino model. S-confining theories with a simple gauge group have been classified. We prove all the S-confining dualities in the list, when the matter fields transform in rank-$1$ and/or rank-$2$ representations. Our only assumptions are the S-confining dualities for $SU(N)$ with $N+1$ flavors and for $Usp(2N)$ with $2N+4$ fundamentals. The strategy consists in a sequence of deconfinements and re-confinements. We pay special attention to the explicit superpotential at each step.