  We study a generalized multichannel single-impurity Kondo model, in which the
impurity spin is described by a representation of the SU(N) group which
combines bosonic and fermionic degrees of freedom. The impurity spin states are
described by Abrikosov pseudofermions, and we make use of a method initiated by
Popov and Fedotov which allows a proper handling of the fermionic constraint.
The partition function is derived within a path integral approach. We use
renormalization group techniques to calculate the $\beta$ scaling function
perturbatively in powers of the Kondo coupling constant, which is justified in
the weak coupling limit. The truncated expansion is valid in the overscreened
(Nozieres-Blandin) regime, for an arbitrary SU(N) group and any value of the
parameters characterizing the impurity spin representation. The intermediate
coupling fixed point is identified. We derive the temperature dependence of
various physical quantities at low T, controlled by a unique critical exponent,
and show that the physics of the system in the overscreened regime governed by
the intermediate coupling fixed point is characterized by a non-Fermi liquid
behavior. Our results are in accordance with those obtained by other methods,
as Bethe ansatz and boundary conformal field theory, in the case of various
impurity spin symmetries. We establish in a unified way that the Kondo models
in which the impurity spin is described successively by a fundamental,
symmetric, antisymmetric and mixed symmetry representation yield all the same
low-energy physics in the overscreened regime. Possible generalizations of the
analysis we present to the case of arbitrary impurity spin representations of
SU(N) are also discussed.
