RENORMALIZATION OF A (2+1)-DIMENSIONAL SUPERSYMMETRIC NONLINEAR SIGMA-MODEL IN 1/N EXPANSION

We explicity carry out the renormalization of the O(N)-invariant supersymmetric nonlinear sigma model up to next-to-leading order in 1/N 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 sigma model. Supersymmetry constrains the anomalous dimensions of the Lagrange multiplier fields to be exactly zero, enabling one to prove renormalizability to all orders in 1/N. Furthermore, the beta function for this model vanishes.