Sigma models with purely Wess-Zumino-Witten actions

We study the dynamics of sigma models in arbitrary dimensions with purely Wess-Zumino-Witten actions (i.e. without kinetic terms), both from the lagrangian and hamiltonian point of view. These models have non-trivial gauge groups which contain the diffeomorphisms of space-time, as well as symmetry groups which in many cases turn out to be infinite dimensional. We give examples in 1, 2, 3 and 4 space-time dimensions.