NONREDUCTIVE WZW MODELS AND THEIR CFTS

We study two-dimensional WZW models with target space a nonreductive L ie group. Such models exist whenever the Lie group possesses a bi-inva riant metric. We show that such WZW models provide a lagrangian descri ption of the nonreductive (affine) Sugawara construction. We investiga te the gauged WZW models and we prove that gauging a diagonal subgroup results in a conformal field theory which can be identified with a co set construction. A large class of exact four-dimensional string backg rounds arise in this fashion. We then study the topological conformal field theory resulting from the G/G coset. We identify the Kazama alge bra extending the BRST algebra, and the BV algebra structure in BRST c ohomology which it induces.