Toulouse limit for the overscreened four-channel Kondo problem

We show that the spin dynamics of the four-channel Kondo model is equivalent to a model with a spin-1/2 impurity coupled to spin-1 conduction electrons. By Abelian bosonization of the latter model we find a kind of Toulouse limit analogous to that recently discussed by Emery and Kivelson for the two-channel case. We analyze the model by exploiting the close analogy to the problem of an impurity in the Luttinger liquid.