A new method to solve the Non Perturbative Renormalization Group equations

TL;DR

This paper introduces a novel approach to solving the Non Perturbative Renormalization Group equations for n-point functions, leveraging mode decoupling and analyticity to simplify the hierarchy of equations.

Contribution

It presents a new method that approximates the RG equations by closing the hierarchy using mode decoupling and background field relations, improving systematically.

Findings

Exact in the large N limit for the O(N) model

Simplifies the derivation of known results without auxiliary fields

Provides a systematic way to improve approximation accuracy

Abstract

We propose a method to solve the Non Perturbative Renormalization Group equations for the $n$-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the $n$-point functions. This is achieved: i) by exploiting the decoupling of modes and the analyticity of the $n$-point functions at small momenta: this allows us to neglect some momentum dependence of the vertices entering the flow equations; ii) by relating vertices at zero momenta to derivatives of lower order vertices with respect to a constant background field. Although the approximation is not controlled by a small parameter, its accuracy can be systematically improved. When it is applied to the O(N) model, its leading order is exact in the large $N$ limit; in this case, one recovers known results in a simple and direct way, i.e., without introducing an auxiliary field.