Current Algebras and Differential Geometry

We show that symmetries and gauge symmetries of a large class of 2-dimensional σ-models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the σ-model. We compute the current-current commutator and analyse the anomaly cancellation condition, which can be interpreted geometrically in terms of Dirac structures, previously studied in the mathematical literature. Generalized complex structures correspond to decompositions of the current algebra into pairs of anomaly free subalgebras. σmodels that we can treat with our method include both physical and topological examples, with and without Wess-Zumino type terms.