Renormalization Group Fixed Points and Connections with Duality in Various Dimensions

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We review some recent results concerning gauge theories in various dimensions. In particular, we discuss RG fixed points and ``mirror'' symmetry duality in 3d N=4 supersymmetric gauge theories and a classification of non-trivial RG fixed points in 5d N=1 supersymmetric theories.
13 pages. Added reference. To appear in Proc. of Puri Conference '96

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