EXACT CONFORMAL-FIELD-THEORY RESULTS ON THE MULTICHANNEL KONDO EFFECT - ASYMPTOTIC 3-DIMENSIONAL SPACE-DEPENDENT AND TIME-DEPENDENT MULTIPOINT AND MANY-PARTICLE GREENS-FUNCTIONS

We have recently developed a conformal field theory approach for quantum impurity problems, which include the multi-channel Kondo effect, allowing us to obtain exact asymptotic Green's functions, amongst other results. The single-fermion Green's function was presented in a separate publication. Here we present the detailed derivation of and explicit expressions for the four-point single-particle and two-point two-particle Green's functions, including the spin-density, charge-density and pair field Green's function. These represent universal crossover functions, from non-interacting (Fermi-liquid) behavior when all operators are far from the impurity, to singular (non-Fermi-liquid) behavior, characterized by Wess-Zumino-Witten conformal field theories, when operators move close to the impurity. These crossover functions show explicitly how ''deconfinement'' of the spin degrees of freedom near the impurity site occurs. The results are obtained for the general case of an SU(N) impurity spin and k channels, using the Fusion Rule of Kac-Moody conformal field theory, modular transformations, the Verlinde formula, and Braid and Fusion matrices. We also show how to compute exact higher multi-point functions with our approach. From the four-point single-particle function we extract an operator product coefficient, needed for the computation of the resistivity. We also present the result for the Wilson ratio for an SU(N) impurity spin.