Anomalous AV^*V vertex function in the soft-wall holographic model of QCD

TL;DR

This paper investigates the anomalous AV*V vertex function in the soft-wall holographic QCD model, comparing it with QCD predictions and examining a proposed relation linking vertex functions to two-point correlators.

Contribution

It provides a holographic QCD calculation of the AV*V vertex functions including the Chern-Simons term and analyzes their relation to QCD and existing theoretical proposals.

Findings

The holographic model reproduces key features of the AV*V vertex functions.

Discrepancies are found between the model and QCD in certain kinematic regimes.

The proposed relation by Son and Yamamoto is critically examined in this context.

Abstract

I consider the three-point function of two vector and one axial-vector currents. In the kinematic configuration in which one of the two vector currents corresponds to an on-shell soft photon, such a vertex is described in QCD by two functions, $w_L$ and $w_T$. After reviewing the properties of these functions in QCD, I describe the result obtained using the soft-wall holographic model of QCD with the addition of the Chern-Simons term and I compare it with the QCD outcome. I also discuss a relation, proposed by Son and Yamamoto, that connects $w_L$ and $w_T$ to the two-point functions $\Pi_{VV}$ and $\Pi_{AA}$.