MANIFOLDS OF FIXED-POINTS AND DUALITY IN SUPERSYMMETRIC GAUGE-THEORIES

There are many physically interesting superconformal gauge theories in four dimensions. In this talk I discuss a common phenomenon in these theories: the existence of continuous families of infrared fixed point s. Well-known examples include finite N = 4 and N = 2 supersymmetric t heories; many finite N = 1 examples are known also. These theories are a subset of a much larger class, whose existence can easily be establ ished and understood using the algebraic methods explained here. A rel ation between the N = 1 duality of Seiberg and duality in finite N = 2 theories is found using this approach, giving further evidence for th e former. This talk is based on work with R. Leigh.