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

TL;DR

This paper employs the exact renormalization group perturbatively to construct the Wilson action for the 2D O(N) non-linear sigma model, addressing regularization of non-linear symmetry with a momentum cutoff.

Contribution

It introduces a perturbative ERG method to construct the Wilson action while managing non-linear symmetry regularization via a Jacobian compensation.

Findings

Successfully regularized non-linear symmetry with momentum cutoff

Generated quadratically divergent potential and compensated its non-invariance

Provided a perturbative framework for constructing the Wilson action

Abstract

We use the exact renormalization group (ERG) perturbatively to construct the Wilson action for the two-dimensional O(N) non-linear sigma model. The construction amounts to regularization of a non-linear symmetry with a momentum cutoff. A quadratically divergent potential is generated by the momentum cutoff, but its non-invariance is compensated by the jacobian of the non-linear symmetry transformation.