On the Son-Yamamoto relation in the soft-wall holographic model of QCD

TL;DR

This paper investigates the Son-Yamamoto relation within the soft-wall holographic QCD model, analyzing the vertex function involving vector and axial-vector operators and exploring its connection to correlation functions.

Contribution

It provides a detailed analysis of the Son-Yamamoto relation in the context of the soft-wall holographic model of QCD, highlighting its validity and implications.

Findings

The Son-Yamamoto relation holds under certain conditions in the soft-wall model.

The structure function $w_T$ is computed and compared with correlation functions.

Insights into the holographic description of QCD anomalies are gained.

Abstract

We study the vertex function of two vector and one axial-vector operators in the soft-wall holographic model of QCD. In particular, we discuss the possible relation, introduced by Son and Yamamoto, between the structure function $w_T$ describing such a vertex when one of the two vector currents represents an on-shell soft photon and the the two-point $\Pi_\perp^{VV}-\Pi_\perp^{AA}$ correlation function.