$U(1)_A$ axial anomaly, $\eta^\prime$, and topological susceptibility in the holographic soft-wall model

TL;DR

This paper explores the $U(1)_A$ axial anomaly and the $ a^ prime$ meson within a holographic soft-wall model, deriving the topological susceptibility and confirming the Witten-Veneziano relation in a bottom-up AdS/QCD approach.

Contribution

It introduces a holographic soft-wall model that captures the axial anomaly and meson mixing, providing new insights into topological susceptibility and meson mass relations.

Findings

$ a^ prime$ mass from mixing of dual fields

Topological susceptibility computed for all quark masses

Witten-Veneziano relation derived in large $N_c$ limit

Abstract

The singlet pseudoscalar sector of light mesons is investigated in the soft-wall model, a bottom-up approach to the AdS/QCD correspondence. The $\eta^\prime$ mass results from the mixing among the fields dual to the axial current, pseudoscalar current and the $G\tilde G$ operator. The topological susceptibility is computed for any quark mass, and the Witten-Veneziano relation is obtained in the large $N_c$ limit.