The Holographic Life of the eta'

TL;DR

The paper presents a holographic model with $N_f$ D6-brane probes in a D4-based background to study eta' physics in large-$N_c$ QCD. It identifies the anomaly-induced eta' potential as arising from open-closed string interactions, with theta-dependence entering only through the combination $\theta + 2\sqrt{N_f}\,\eta'/f_\pi$, and verifies this structure by a detailed 1/\sqrt{N_c} check of the linear term in the eta' potential via two independent computations. The work derives non-derivative eta'-glueball couplings from RR-sector fluctuations and demonstrates explicit mixing with pseudoscalar glueballs, consistent with the Witten-Veneziano mass scale $m_{\eta'}^2 \sim (N_f/N_c)$ and the topological susceptibility $\chi_{YM}$. The results provide a coherent string-theoretic realization of the U(1)_A anomaly and its consequences for eta' phenomenology in holographic QCD, with implications for UV/IR consistency and potential Green-Schwarz-like interpretations of the RR couplings.

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.