EXACTLY MARGINAL OPERATORS AND DUALITY IN 4-DIMENSIONAL N=1 SUPERSYMMETRIC GAUGE-THEORY

We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N = 1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these ope rators, using tools similar to those employed in two-dimensional N = 2 supersymmetry. In particular we rely on the work of Shifman and Vains htein relating the beta-function of the gauge coupling to the anomalou s dimensions of the matter fields. Finite N = 1 models, which have mar ginal operators at zero coupling, are easily identified using our appr oach. The method can also be employed to find manifolds of fixed point s which do not include the free theory; these are seen in certain mode ls with product gauge groups and in many non-renormalizable effective theories. For a number of our models, S-duality may have interesting i mplications, Using the fact that relevant perturbations often cause on e manifold of fixed points to flow to another, we propose a specific m echanism through which the N = 1 duality discovered by Seiberg could b e associated with the duality of finite N = 2 models.