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Abstract We consider 5d KK dualities, that is multiple 5d gauge theories with the same 6d infinite coupling limit. We provide a prescription to associate 4d N $$ \mathcal{N} $$ = 1 quivers to the 5d dual quivers, such that the 4d quivers are also dual to each other. The 4d dualities are infrared dualities which can be checked matching global symmetry anomalies and in certain cases can be proven using basic Seiberg dualities sequentially. We also consider dualities obtained by Higgsing in two different ways the same 5d theory, in some simple examples.

Abstract We propose new classes of 4d N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 1 theory that flows to the conformal manifold of N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 1 theory that flows to the conformal manifold of a 4d N $$ \mathcal{N} $$ = 2 necklace theory with SU(2n + 1)3 gauge group.

Abstract We consider four dimensional N $$ \mathcal{N} $$ = 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.

Abstract We apply the technique of sequential deconfinement to the four dimensional N $$ \mathcal{N} $$ = 1 U sp(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 U sp(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 N $$ \mathcal{N} $$ = 2 theories, recovering known fully deconfined duals of U sp(2N) and U(N) gauge theories, and obtaining new ones.