New spin-2 gauged sigma models and general conformal field theory

Recently, we have studied the general Virasoro construction at one loop in the background of the general nonlinear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-2 gauged sigma models. As examples of the new actions, we discuss the spin-2 gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-2 gauged g/h coset constructions. We are able to identify the latter as the actions of the local Lie h-invariant conformal field theories, a large class of generically irrational conformal field theories with a local gauge symmetry.