Conformal field theories and twisted Kac-Moody algebras

In the first part of this work we generalize the standard b-c model to accommodate for rational values of the conformal weight. This leads to the construction of conformally invariant models with rational values of their central charge. This geometric construction holds both for non-twisted and twisted boundary conditions. In the latter case we give a free field construction of the currents which satisfy the commutation rules of a twisted Kac-Moody algebra for arbitrary value of the level k and, in the case of SU(2) centrally extended, we compute the conformal blocks on the sphere. These are the conformal blocks of the orbifold given by SU(2) modded out by Z2. We also discuss the relevance of all this to the definition of hierarchies of differential equations admitting solitonic solutions