  We introduce a representation of electron operators as a product of a
spin-carry ing fermion and of a phase variable dual to the total charge (slave
quantum rotor). Based on this representation, a new method is proposed for
solving multi-orbital Anderson quantum impurity models at finite interaction
strength U. It consists in a set of coupled integral equations for the
auxiliary field Green's functions, which can be derived from a controlled
saddle-point in the limit of a large number of field components. In contrast to
some finite-U extensions of the non-crossing approximation, the new method
provides a smooth interpolation between the atomic limit and the weak-coupling
limit, and does not display violation of causality at low-frequency. We
demonstrate that this impurity solver can be applied in the context of
Dynamical Mean-Field Theory, at or close to half-filling. Good agreement with
established results on the Mott transition is found, and large values of the
orbital degeneracy can be investigated at low computational cost.
