Mathcal{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 G2 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: T4, R0,4, R2,5, and rank 2n Minahan-Nemeschansky E6 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.