Flow of low energy couplings in the Wilson renormalization group

TL;DR

This paper introduces a novel form of the Wilson renormalization group equation that reveals a gradient flow structure for low-energy couplings, providing new insights into the behavior of marginal couplings in quantum field theories.

Contribution

The paper derives a new Wilson RG equation form where the flow is proportional to a gradient, and identifies coordinates where marginal couplings follow a gradient flow when relevant couplings are tuned to zero.

Findings

Flow equations are proportional to a gradient flow up to linear terms.

A coordinate system is found where marginal couplings follow a gradient flow.

The gradient flow structure emerges when relevant couplings are tuned to vanish.

Abstract

A new form of the Wilson renormalization group equation is derived, in which the flow equations are, up to linear terms, proportional to a gradient flow. A set of co\"ordinates is found in which the flow of marginal, low-energy, couplings takes a gradient form, if relevant couplings are tuned to vanish.