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Journal of High Energy Physics

, 2019:46 | Cite as

\( \mathcal{N} \) = 1 conformal dualities

  • Shlomo S. RazamatEmail author
  • Gabi Zafrir
Open Access
Regular Article - Theoretical Physics
  • 22 Downloads

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.

Keywords

Conformal Field Theory Duality in Gauge Field Theories Supersymmetric Gauge Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsTechnionHaifaIsrael
  2. 2.IPMUUniversity of TokyoKashiwaJapan
  3. 3.Kavli IPMU (WPI), UTIASUniversity of TokyoKashiwaJapan

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