  Whereas the theoretical results for the dominant contributions to hadronic
light-by-light scattering coming from pseudoscalar meson exchange have
converged over the past years, the various published estimates of the
contribution due to axial vector meson exchange differ wildly. Since
holographic AdS/QCD models have proved to provide rather good models of singly
and doubly virtual pion transition form factors, which reproduce remarkably
well the known low-energy data and also the asymptotic leading-order pQCD
behavior, it is of interest to consider their predictions for axial vector
transition form factors. Indeed, we find that these reproduce also very well
existing data from the L3 experiment for $f_1\to\gamma\gamma^*$. Including the
full infinite tower of axial vector mesons of the AdS/QCD models we moreover
show that the Melnikov-Vainshtein short-distance constraint can be satisfied,
while almost all existing models for hadronic light-by-light scattering fail to
incorporate it. The contribution to $g-2$, which is dominated by the first few
resonances, turns out to be significantly larger than estimated previously.
