Deformed minimal models and generalized Toda theory

We introduce a generalization of A_r-type Toda theory based on a non-Abelian group G, which we call the (A_r, G)-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine (A₁, SU(2))-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator Φ_(2,1). We derive infinite conserved charges and soliton solutions from the Lax pair of the affine (A₁, SU(2))-Toda theory. Another type of integrable deformation which accounts for the Φ_(3,1)-deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.