Witten-Veneziano from Green-Schwarz
Adi Armoni
TL;DR
The paper tackles the U(1) problem by embedding it in AdS/CFT with flavor, proposing that the $\eta'$ meson is the twisted-sector RR field $C_A$ responsible for canceling the axial anomaly via a generalized Green–Schwarz mechanism. Using a D3-brane setup on the orbifold ${f C}^3/({\mathbb Z}_3\otimes{\mathbb Z}_3)$, the author derives the Witten–Veneziano formula for the $\eta'$ mass from holography, connecting the bulk anomaly-canceling mode to the boundary $ ext{tr} F\tilde F$ correlator and the axial current via the anomaly equation. The derivation shows that in the appropriate large-$N$ limit and in the presence of flavors, the $ ext{tr} F\tilde F$ correlator decomposes into bulk (glueball) and meson contributions, with the axial bulk mode acquiring a mass consistent with $M_{\,\eta'}^2$. This work provides a holographic interpretation of the WV mechanism, highlighting the role of twisted RR fields in anomaly cancellation and enabling explicit computations in orbifold-based AdS/CFT models. It broadens the understanding of how anomalous symmetries and their breaking are realized in string-theoretic duals and suggests avenues for quantitative eta-prime mass calculations in specific holographic setups.
Abstract
We consider the U(1) problem within the AdS/CFT framework. We explain how the Witten-Veneziano formula for the eta' mass is related to a generalized Green-Schwarz mechanism. The closed string mode, that cancels the anomaly of the gauged U(1) axial symmetry, is identified with the eta' meson. In a particular set-up of D3-branes on a C3/(Z3xZ3) orbifold singularity, the eta' meson is a twisted-sector R-R field.