S-confining gauge theories and supersymmetry enhancements

Abstract: We propose new classes of $4d$ $\mathcal{N}!=!1$ S-confining gauge theories, with a simple gauge group, rank-two matter and cubic superpotentials. The gauge group can be symplectic, orthogonal or special unitary. In some cases we derive the dualities via the deconfinement technique that uses iteratively known, more fundamental, dualities. In the symplectic case we discuss the $3d$ reduction to a confining unitary gauge theory with monopole superpotential. This $3d$ S-confinement provides an understanding of a recently proposed $4d$ $\mathcal{N}!=!1$ theory that flows to the conformal manifold of $\mathcal{N}!=!4$ SYM with $SU(2n+1)$ gauge group. The $3d$ perspective allows us to generalize this construction to another similar flow with supersymmetry enhancement: a $4d$ $\mathcal{N}!=!1$ theory that flows to the conformal manifold of a $4d$ $\mathcal{N}!=!2$ necklace theory with $SU(2n+1)^3$ gauge group.