Perturbative renormalization of the CPsup(N) model

Within an unusual but very convenient parametrization of the fields we show the perturbative renormalizability of the CPsup(N) model. This is first worked out with traditional dimensional renormalization techniques: one finds there is a unique divergence related to an equal coupling constant and mass renormalization while the field and its transformation law are not renormalized. In a second part we use BPHZ renormalization, strengthened by BRS consistency constraints, to obtain the relevant Ward identity for the non-linear symmetry of the model. (orig.)