Ultraviolet finiteness of the Wess-Zumino-Witten gauge model on homogeneous manifolds

In the nonlinear two-dimensional model, whose action is the sum of actions of two Wess-Zumino-Witten models and of the interaction of a special kind between them, the classical energy-momentum tensor is expressed in terms of conserved currents. For the Virasoro algebra generated by the tensor to have a constant central charge in quantum theory, it is required that the theory by finite. It is shown by means of an explicit calculation of one- and two-loop counterterms that this is the case only for a special choice of parameters for which the model is gauge-invariant and is defined on a homogeneous space.