Magnetic Impurity in a Luttinger Liquid: A Conformal Field Theory Approach

We study the low-temperature properties of a spin-\onehalf\ magnetic impurity coupled to a one-dimensional interacting electron system. Using the newly developed formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for non-interacting electrons, but with a novel Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward- and backward scattering {\em (Kondo interaction)}, we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: {\em either} a local Fermi liquid {\em or} a critical theory with an anomalous specific heat. The latter case agrees with a recent ``poor-man-scaling'' result proposed by Furusaki and Nagaosa.