New Superconformal Field Theories in Four Dimensions and N=1 Duality

TL;DR

This paper introduces new four-dimensional superconformal field theories and non-Abelian duality phenomena in N=1 supersymmetric gauge theories, highlighting their non-perturbative dynamics and potential implications for understanding QCD.

Contribution

It provides a pedagogical overview of emergent superconformal theories and dualities in N=1 supersymmetric gauge models, including new phenomena in SO and Sp gauge theories.

Findings

Discovery of new superconformal field theories in 4D

Identification of non-Abelian electric-magnetic duality at IR fixed points

Observation of novel non-perturbative phenomena like oblique confinement

Abstract

Recently, developments in the understanding of low-energy N=1 supersymmetric gauge theory have revealed two important phenomena: the appearance of new four-dimensional superconformal field theories and a non-Abelian generalization of electric-magnetic duality at the IR fixed point. This report is a pedagogical introduction to these phenomena. After presenting some necessary background material, a detailed introduction to the low-energy non-perturbative dynamics of N=1 supersymmetric $SU(N_c)$ QCD is given. The emergence of new four-dimensional superconformal field theories and non-Abelian duality is explained. New non-perturbative phenomena in supersymmetric $SO(N_c)$ and $Sp(N_c=2n_c)$ gauge theories, such as the two inequivalent branches, oblique confinement and electric-magnetic-dyonic triality, are presented. Finally, some new features of these four-dimensional superconformal field theories are exhibited: the universal operator product expansion, evidence for a possible $c$-theorem in four dimensions and the critical behaviour of anomalous currents. The concluding remarks contain a brief history of electric-magnetic duality and a discussion on the possible applications of duality to ordinary QCD.