Superconformal current algebras and topological field theories

Topological conformal field theories based on superconformal current algebras are constructed. The models thus obtained are the supersymmetric version of the $G/G$ coset theories. Their topological conformal algebra is generated by operators of dimensions $1$, $2$ and $3$ and can be regarded as an extension of the twisted $N=2$ superconformal algebra. These models possess an extended supersymmetry whose generators are exact in the topological BRST cohomology.