Renormalization of a (2 + 1)-dimensional supersymmetric nonlinear model in 1N expansion.

We explicitly carry out the renormalization of the O(N)-invariant supersymmetric nonlinear model up to next-to-leading order in 1N and show that the wave-function renormalization removes all divergences. Cancellations between fermion and boson loops prevent counterterms from being induced which would otherwise spoil the nonlinear constraint. This aspect leads to the renormalization of the model by the conventional Bogoliubov-Parasiuk-Hepp-Zimmermann scheme in contrast with the ordinary nonlinear model. Supersymmetry constrains the anomalous dimensions of the Lagrange multiplier fields to be exactly zero, enabling one to prove renormalizability to all orders in 1N. Furthermore, the function for this model vanishes. © 1991 The American Physical Society.