The Holographic Life of the eta'

TL;DR

This paper investigates the holographic dual description of the eta' meson in large-N_c QCD, identifying string diagrams responsible for its mass generation and confirming theoretical predictions through quantitative analysis.

Contribution

It identifies the string diagrams responsible for eta' mass in holographic QCD and relates them to pseudoscalar glueball mixings, providing a detailed holographic analysis.

Findings

Mass of eta' arises from specific string diagrams.

Agreement with Witten-Veneziano formula for eta' mass.

Dependence on theta-angle matches U(1) anomaly predictions.

Abstract

In the string holographic dual of large-N_c QCD with N_f flavours of Kruczenski et al, the eta' meson is massless at infinite N_c and dual to a collective fluctuation of N_f D6-brane probes in a supergravity background. Here we identify the string diagrams responsible for the generation of a mass of order N_f/N_c, consistent with the Witten-Veneziano formula, and show that the supregravity limit of these diagrams corresponds to mixings with pseudoscalar glueballs. We argue that the dependence on the theta-angle in the supergravity description occurs only through the combination theta + 2 \sqrt{N_f} eta' / f_pi, as dictated by the U(1) anomaly. We provide a quantitative test by computing the linear term in the eta' potential in two independent ways, with perfect agreement.