Infinitely many N=1 dualities from m+1-m=1

Abstract

We discuss two infinite classes of 4d supersymmetric theories, T-N((m)) and u(N)((m)), labelled by an arbitrary non-negative integer, m. The T-N((m)) theory arises from the 6d, A(N-1) type N=(2,0) theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree (m+1, -m); the m=0 case is the N=2 supersymmetric T-N theory. The novelty is the negative-degree line bundle. The u(N)((m)) theories likewise arise from the 6d N=(2,0) theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) T-N((m)) theories. The T-N((m)) and u(N)((m)) theories can be represented, in various duality frames, as quiver gauge theories, built from T-N components via gauging and nilpotent Higgsing. We analyze the RG flow of the u(N)((m)) theories, and find that, for all integer m>0, they end up at the same IR SCFT as SU(N) SQCD with 2N flavors and quartic superpotential. The u(N)((m)) theories can thus be regarded as an infinite set of UV completions, dual to SQCD with N-f=2N(c). The u(N)((m)) duals have different duality frame quiver representations, with 2m+1 gauge nodes.