The geometry of supersymmetric coset models and superconformal algebras

An on-shell formulation of (p,q), 2\leq p \leq 4, 0\leq q\leq 4, supersymmetric coset models with target space the group G and gauge group a subgroup H of G is given. It is shown that there is a correspondence between the number of supersymmetries of a coset model and the geometry of the coset space G/H. The algebras of currents of supersymmetric coset models are superconformal algebras. In particular, the algebras of currents of (2,2) and (4,0) supersymmetric coset models are related to the N=2 Kazama-Suzuki and N=4 Van Proeyen superconformal algebras correspondingly.