  Several Quantum Impurity problems with four flavors of bulk fermions have
zero temperature fixed points that show non fermi liquid behavior. They include
the two channel Kondo effect, the two impurity Kondo model, and the fixed point
occurring in the four flavor Callan-Rubakov effect. We provide a unified
description which exploits the SO(8) symmetry of the bulk fermions. This leads
to a mapping between correlation functions of the different models.
Furthermore, we show that the two impurity Kondo fixed point and the
Callan-Rubakov fixed point are the same theory. All these models have the
puzzling property that the S matrix for scattering of fermions off the impurity
seems to be non unitary. We resolve this paradox showing that the fermions
scatter into collective excitations which fit into the spinor representation of
SO(8). Enlarging the Hilbert space to include those we find simple linear
boundary conditions. Using these boundary conditions it is straightforward to
recover all partition functions, boundary states and correlation functions of
these models.
