Kondo effect in a luttinger liquid: nonuniversality of the wilson ratio

Using a coset Ising-Bose representation, we show how backscattering of electrons off a magnetic impurity destabilizes the two-channel Kondo fixed point and drives the system to a new fixed point, in agreement with previous results [P. Fröjdh and H. Johannesson, Phys. Rev. Lett. 75, 300 (1995)]. In addition, we find that the presence of several leading correction-to-boundary operators in the spinon basis, for nonzero U, implies a not well-defined Wilson ratio. Finally, we show that a strong potential scattering at the impurity site stabilizes the two-channel Kondo fixed point in the neighborhood of half-filling.