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(Nc) 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(Nc) and Sp(Nc = 2nc) 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. Address after September 1, 2000: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1 On leave from the Theoretical Physics Division, Department of Physics, University of Helsinki