Son-Yamamoto relation and Holographic RG flows

TL;DR

This paper investigates the Son-Yamamoto relation within holographic QCD models, analyzing how it behaves under RG flows using Hamilton-Jacobi equations, and finds it remains diagonal in certain models but not others.

Contribution

It demonstrates the behavior of the Son-Yamamoto relation under RG flows in holographic models, highlighting differences between models with and without scalar fields.

Findings

Son-Yamamoto relation is RG flow diagonal in 5d YM-CS model

In models with scalar fields, the RG equation gains an inhomogeneous term

Analysis uses Hamilton-Jacobi formalism for holographic RG flows

Abstract

Motivated by the Son-Yamamoto (SY) relation which connects the three point and two-point correlators we consider the holographic RG flows in the bottom-up approach to holographic QCD via the Hamilton-Jacobi (HJ) equation with respect to the radial coordinate . It is shown that the SY relation is diagonal with respect to the RG flow in the 5d YM-CS model while the RG equation acquires the inhomogeneous term in the model with the additional scalar field which encodes the chiral condensate.