N=1 conformal dualities

Abstract

We consider on one hand the possibility that a supersymmetric $\mathcal{N}=1$ conformal gauge theory has a strongly coupled locus on the conformal manifold at which a different, dual, conformal gauge theory becomes a good weakly coupled description. On the other hand we discuss the possibility that strongly coupled theories, e.g. SCFTs in class $\mathcal{S}$, having exactly marginal $\mathcal{N}=1$ deformations admit a weakly coupled gauge theory description on some locus of the conformal manifold. We present a simple algorithm to search for such dualities and discuss several concrete examples. In particular we find conformal duals for $\mathcal{N}=1$ SQCD models with $G_2$ gauge group and a model with $SU(4)$ gauge group in terms of simple quiver gauge theories. We also find conformal weakly coupled quiver theory duals for a variety of class $\mathcal{S}$ theories: $T_4$, $R_{0,4}$, $R_{2,5}$, and rank $2n$ Minahan-Nemeschansky $E_6$ theories. Finally we derive conformal Lagrangians for four dimensional theories obtained by compactifying the E-string on genus $g>1$ surface with zero flux. The pairs of dual Lagrangians at the weakly coupled loci have different symmetries which are broken on a general point of the conformal manifold. We match the dimensions of the conformal manifolds, symmetries on the generic locus of the conformal manifold, anomalies, and supersymmetric indices. The simplicity of the procedure suggests that such dualities are ubiquitous.

14 pages, 13 figures, revtex; v2: footnote 1 added

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• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Star shaped quivers with flux
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
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• Conformal S-dualities from O-planes
• Non minimal D-type conformal matter compactified on three punctured spheres
• A Nilpotency Index of Conformal Manifolds
• A CFT Distance Conjecture
• Emergent N=4 supersymmetry from N=1
• No go for a flow
• Geometric Approach to 3D Interfaces at Strong Coupling
• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• $\mathcal{N}=1$ conformal dualities from unoriented chiral quivers
• Aspects of 4d supersymmetric dynamics and geometry