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

Abstract

We discuss two infinite classes of 4d supersymmetric theories, $T_N^{(m)}$ and ${\mathcal{U}}_N^{(m)}$, labelled by an arbitrary non-negative integer, $m$. The $T_N^{(m)}$ theory arises from the 6d, $A_{N-1}$ type $\mathcal{N}=(2,0)$ 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 $\mathcal{N}=2$ supersymmetric $T_N$ theory. The novelty is the negative-degree line bundle. The ${\mathcal{U}}_N^{(m)}$ theories likewise arise from the 6d $\mathcal{N}=(2,0)$ 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 ${\mathcal{U}}_N^{(m)}$ 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 ${\mathcal{U}}_N^{(m)}$ 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 ${\mathcal{U}}_N^{(m)}$ theories can thus be regarded as an infinite set of UV completions, dual to SQCD with $N_f=2N_c$. The ${\mathcal{U}}_N^{(m)}$ duals have different duality frame quiver representations, with $2m+1$ gauge nodes.

42 pages, 30 figures

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• $\mathcal{N}=1$ superconformal theories with $D_N$ blocks
• 4d N=1 from 6d N=(1,0) on a torus with fluxes
• Infinitely many 4d N=1 SCFTs with a=c
• Rank $Q$ E-String on Spheres with Flux