Lattice conformal theories and their integrable perturbations

Abstract We study the lattice analogues of the Wess-Zumino-Witten (WZW) and Toda conformal field theories. We describe discrete versions of the Drinfel'd-Sokolov reduction and the Sugawara construction for the WZW model, and show how to formulate a perturbation theory in the chiral sector. We describe the spaces of integrals of motion of the perturbed theories. We interpret the perturbed WZW model in terms of NLS hierarchy and obtain an embedding of this model into the lattice KP hierarchy.