New formulations of the solutions of N=1 and N=2 super Toda field theory are introduced, using Hamiltonian reduction of the N=1 and N=2 super WZNW Models to the super Toda Models. These pa-rameterisations are then used to present the Hamiltonian formulations of the super Toda theories on the spaces of solutions.

The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is selfcontained, elementary and is tailor-made for the application. It is well-known that the Liouville equation for a smooth, real field φ under periodic boundary condition is a reduction of the SL(2,R) WZNW model on the cylinder, wh...

We consider the supersymmetric WZNW model gauged in a manifestly supersymmetric way. We find the BRST charge and the necessary condition for nilpotency. In the BRST framework the model proves to be a Lagrangian formulation of the supersymmetric coset construction, known as the N=1 Kazama-Suzuki coset construction.

It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decoupled β-γ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity of versions of the corresponding ordinary models and decoupled abelian fields.

We find some exact solutions of the Knizhnik-Zamolodchikov equation for the four point correlation functions that occur in the SL(2, R) WZNW model. They exhibit logarithmic behaviour in both the Kac-Moody and Virasoro parts. We discuss their implication for the operator product expansion. We also observe the appearance of several symmetries of the correlation functions. [email protected]...