Toulouse limit for the overscreened four-channel Kondo problem

We show that the spin dynamics of the 4--channel Kondo model is equivalent to the one of 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 2--channel case. We analyse the model by exploiting the close analogy to the problem of an impurity in the Luttinger liquid.