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 Kähler type. 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.