Two-node Dualities from Elementary Dualities in 3d and 4d

Abstract

A new 3d $\mathcal{N}=2$ two-node Seiberg-like duality, analogous to the 4d $\mathcal{N}=1$ Intriligator--Leigh--Strassler~(ILS) duality, is proposed. As strong evidence, we check the agreement between the 3d $\mathcal{N}=2$ ellipsoid partition functions for numerous cases using s-confinement method. Surprisingly, our derivation assumes only two elementary 3d $\mathcal{N}=2$ dualities: Aharony and Benini--Benvenuti--Pasquetti, which reinforces the idea dualities from dualities. We also revisit the original ILS duality and provide a derivation based on nodewise dualities. In particular, we apply a sequence of Seiberg and Kutasov--Schwimmer dualities to individual gauge nodes, with Higgsing at an intermediate step, and subsequently integrate out the massive fields.