The Holographic Life of the η

In the string holographic dual of large-Nc QCD with Nf ∞avours of (1), the · 0 meson is massless at inflnite Nc and dual to a collective ∞uctuation of Nf D6-brane probes in a supergravity background. Here we identify the string diagrams responsible for the gen- eration of a mass of order Nf=Nc, consistent with the Witten-Veneziano formula, and show that the supergravity limit of these diagrams corresponds to mixings with pseudoscalar glueballs. We argue that the dependence on the µ-angle in the supergravity description occurs only through the combination µ + 2 p Nf· 0 =f…, as dictated by the U(1)A anomaly. We provide a quantitative test by computing the linear term in the · 0 potential in two independent ways, with perfect agreement.