Integrable Lorentz-breaking deformations and RG flows

We construct the all loop effective action for WZW models perturbed by current-bilinear terms of the type $J_+J_-$, $J_+J_+$ and $J_-J_-$, the last two of which explicitly break Lorentz invariance. For isotropic couplings we prove integrability. For the case in which only the first two terms are present we identify a non-perturbative symmetry of the effective action and we compute the exact beta-functions. These become identically zero outside a bounded region in the parametric space.