  We construct the boundary conformal field theory that describes the
low-temperature behavior of the two-channel Anderson impurity model. The
presence of an exactly marginal operator is shown to generate a line of stable
fixed points parameterized by the charge valence of the impurity. We calculate
the exact zero-temperature entropy and impurity thermodynamics along the fixed
line. We also derive the critical exponents of the characteristic Fermi edge
singularities caused by time-dependent hybridization between conduction
electrons and impurity. Our results suggest that in the mixed-valent regime the
electrons participate in two competing processes, leading to frustrated
screening of spin and channel degrees of freedom. By combining the boundary
conformal field theory with the Bethe Ansatz solution we obtain a complete
description of the low-energy dynamics of the model.
