The Ka-Moody anomaly. An obstruction to a gauged Wess-Zumino-Witten model

We present a gauged Wess-Zumino-Witten model, in which the topological term is a difference of Chern-Simons forms. Part of the Ka-Moody currents become first-class constraints, thus generating local Ka-Moody symmetries. This model provides a lagrangian relization of the Goddard-Kent-Olive coset construction. At the quantum level, however, the Ka-Moody anomaly vanishes only for a negative value of the central charge k.