New superconformal field theories in four dimensions and N=1 duality

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 held 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. (C) 2001 Elsevier Science B.V. All rights reserved.