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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 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.