  We construct a string-inspired model for the central production of $\eta$ and
$\eta'$ mesons in proton-proton collisions, via double Pomeron exchange. Using
general symmetry considerations, we construct a low-energy differential cross
section for double glueball exchange in terms of some undetermined coupling
constants and form factors. We extend this model to the Regge regime, replacing
the glueball propagators with Pomeron trajectories, and modifying the
interaction term by a factor derived from the 5-string scattering amplitude in
flat space. We then fix the couplings which remain undetermined, using the
Sakai-Sugimoto framework to model low-energy QCD. Finally, we generate a
simulation of the scattering process at $\sqrt{s} = 29.1 GeV$, where double
Pomeron exchange should play a role (secondary to double Reggeon exchange). We
focus on the dependence of the scattering cross section on the angle between
the scattered protons in the transverse plane. The results exhibit a definite
deviation from the angular dependence that arises as a consequence of natural
parity violation alone. The amount of deviation is primarily determined by
couplings that come from the Chern-Simons action of the AdS/QCD supergravity
dual, which is directly related to the QCD gravitational anomaly, and thus
constitutes a universal part of any five-dimensional string/gravity dual theory
of QCD. We argue that this makes the high energy central production of
pseudoscalar mesons an interesting probe of AdS/QCD models.
