DIMENSIONAL REGULARIZATION IN THE 1/N EXPANSION

Abstract

Two classes of renormalizable 1/N expandable two-dimensional models are analyzed to O(1/N) and the asymptotic behavior of the renormalized two-point functions is nonperturbatively evaluated. These results are taken as a benchmark to study the applicability of dimensional regularization and perturbative minimal subtraction renormalization to the context of the 1/N expansion. Perturbation theory is applied to O(1/N) diagrams to all orders in the weak coupling constant and, after resummation, the same finite renormalization group invariant asymptotic amplitudes are obtained. As a byproduct, the O(1/N) contributions to renormalization group Z functions in the minimal subtraction scheme are extracted and the critical index η is evaluated and compared to previous nonperturbative results, finding complete agreement. The appendix is devoted to the extension of these results to a supersymmetric version of the models.