Regularization ambiguities of the nonlinearσmodel in 2 and 2+εdimensions

Evaluation of the one-loop effective action of the two-dimensional nonlinear model is carried out using both dimensional regularization and a recently developed scheme called operator regularization, which allows all calculations to be carried out in exactly two dimensions. We find that in operator regularization all quantities associated with the effective action are uniquely determined, whereas in dimensional regularization we find that certain quantities are inherently ambiguous. We comment on the origin and nature of such ambiguities, and their implications for evaluation of the trace anomaly.