Perturbative construction of the two-dimensional O(N) nonlinear sigma modelwith 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 symmetrywith a momentum cutoff. We nd out that the model is parameterized by three functions. We show how to tune them byimposing the Ward{Takahashi (WT) identity. We construct two composite operators that generate in nitesimal changeof the coupling constant and the renormalization of the scalar elds. Finally we show how the beta functions and theanomalous dimensions arise in the model up to 1-loop.