  We study the Kondo effect in two crossed Luttinger liquids, using Boundary
Conformal Field Theory. We predict two types of critical behaviors: either a
two-channel Kondo fixed point with a nonuniversal Wilson ratio, or a new theory
with an anomalous response identical to that found by Furusaki and Nagaosa (for
the Kondo effect in a single Luttinger liquid). Moreover, we discuss the
relevance of perturbations like channel anisotropy, and we make links with the
Kondo effect in a two-band Hubbard system modeled by a channel-dependent
Luttinger Hamiltonian. The suppression of backscattering off the impurity
produces a model similar to the four-channel Kondo theory.
