N 3/2 scaling from 3d N = 2 dualities: an alternative approach to chiral quivers

A bstract We investigate families of 3d N N = 2 chiral quiver gauge theories conjectured to be dual to M2-branes probing toric SE 7 singularities. Geometrically, these families correspond to toric diagrams without internal points. At the field theory level, the models are constructed via an un-higgsing procedure applied to non-chiral quivers. While the moduli space of these theories was shown to match M-theory expectations, determining the N 3/2 scaling of the free energy remained an open problem for over a decade, with positive results emerging only very recently. In this work, we address this challenge by reformulating the three-sphere partition function as a hyperbolic hypergeometric integral. Using exact integral identities, we show that the free energy reduces at leading order in N to that of non-chiral quivers with chiral flavors, for which the N 3/2 scaling is already established. Physically, this mathematical identity corresponds to the equivalence of three-sphere partition functions under a generalization of Giveon-Kutasov duality to chiral quivers.