N=4 SUPERCONFORMAL ALGEBRAS AND GAUGED WESS-ZUMINO-WITTEN MODELS

As shown by Witten the N = 1 supersymmetric gauged Wess-Zumino-Witten (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 Kahler type. We extend Witten's result and prove that the N = 1 supersymmetric gauged WZW models over G x U(1) are actually invariant under N = 4 superconformal transformations if the gauged subgroup H is such that G/[H x SU(2)] is a quaternionic symmetric space. A previous construction of ''maximal'' N = 4 superconformal algebras with SU(2) x SU(2) x 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.