Transition from overscreening to underscreening in the multichannel Kondo model: exact solution at large N

A novel large-N limit of the multichannel Kondo model is introduced, for representations of the impurity spin described by Schwinger bosons. Three cases are found, associated with underscreening, overscreening and exact Kondo screening of the impurity. The saddle-point equations derived in this limit are reminiscent of the ``non-crossing approximation'', but preserve the Fermi-liquid nature of the model in the exactly screened case. Several physical quantities are computed, both numerically, and analytically in the low-\omega,T limit, and compared to other approaches.