Gauged WZW Models

As shown by Witten the N = 1 supersymmetric gauged WZW model based on a group G has an extended N = 2 supersymmetry if the gauged subgroup H is so chosen that G/H is Kähler. We extend Witten’s result and prove that the N = 1 supersymmetric gauged WZW models over G×U(1) are actually invariant under N = 4 superconformal transformations if the gauged subgroup H is such that G/(H × SU(2)) is a quaternionic symmetric space. A previous construction of “maximal” N = 4 superconformal algebras with SU(2) × SU(2) × U(1) symmetry is reformulated and further developed so as to relate them to the N = 4 gauged WZW models. Based on earlier results we expect the quantization of N = 4 gauged WZW models to yield the unitary realizations of maximal N = 4 superconformal algebras provided by this construction. () Work supported in part by the National Science Foundation Grant PHY-9108286. Permanent Address: Physics Department, Penn State University, University Park, PA 16802 e-mail: [email protected] or [email protected]