Renormalization group flows in generalized Toda field theories

We study the scaling properties and renormalization-group flows of models that describe SU(N) Toda field theories in the presence of a background charge. In the Kosterlitz-Thouless region the N > 2 affine Toda theory is not renormalizable and additional couplings must be included. We consider the SU(3) case in detail and compute in perturbation theory the renormalization group beta-functions. We exhibit RG trajectories connecting UV and IR fixed points where the central charge matches the values of the central charge of conformal field theories with a W₃ algebra. Finally, we generalized out results to arbitrary N.