Topological current algebras in two dimensions

Abstract 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.