Perturbative construction of the two-dimensional O(N) nonlinear sigma model with ERG

Abstract

We use the exact renormalization group (ERG) perturbatively to construct the Wilson action for the two-dimensional O(N) nonlinear sigma model (NLSM). The construction amounts to regularization of a nonlinear symmetry with a momentum cutoff. We find out that the model is parameterized by three functions. We show how to tune them by imposing the Ward--Takahashi (WT) identity. We construct two composite operators that generate infinitesimal change of the coupling constant and the renormalization of the scalar fields. Finally we show how the beta functions and the anomalous dimensions arise in the model up to 1-loop.