  A mapping between fractional quantum Hall (FQH) junctions and the two-channel
Kondo model is presented. We discuss in detail this relation for the particular
case of a junction of a FQH state at $\nu = 1/3$ and a normal metal. We show
that in the strong coupling regime this junction has a non-Fermi liquid fixed
point. At this fixed point the electron Green's function has a branch cut, and
the entropy has a non-zero value equal to $S={1/2} \ln{2}$. We construct the
space of perturbations at the strong coupling fixed point and find that the
dimensions of the tunneling operator is 1/2. These behaviors are strongly
reminiscent of the non-Fermi liquid fixed point of a number of quantum impurity
models, particularly the two-channel Kondo model. However we have found that,
in spite of these similarities, the Hilbert spaces of these two systems are
quite different. In particular, although in a special limit the Hamiltonians of
both models are the same, their Hilbert spaces are not since they are
determined by physically distinct boundary conditions. As a consequence the
spectrum of operators in both models is different.
