Topological current algebras in two dimensions

Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the $N=2$ superconformal models and contains generators of dimensions $1$, $2$ and $3$ that close a linear algebra. Our construction can be carried out with one and two bosonic currents and the resulting theories can be interpreted as topological sigma models for group manifolds