Exact results for the Kondo effect in a Luttinger liquid

The Kondo effect in a Luttinger liquid composed of right-moving, spin-up electrons and left-moving, spin-down electrons is mapped exactly onto the Kondo effect in a Fermi liquid. The transformation generates anisotropy in the exchange coupling, which explains the two most notable features of the Kondo effect in a full Luttinger liquid: the quenching of the impurity moment for ferromagnetic, as well as antiferromagnetic, exchange and a power-law dependence of the Kondo temperature on the exchange coupling. Impurity contributions to the low-energy thermodynamics have the same temperature dependence as in a Fermi liquid.