Superconnections in AdS/QCD and the hadronic light-by-light contribution to the muon $g-2$

In this paper, we consider hard-wall AdS/QCD models extended by a string-theory inspired Chern-Simons action in terms of a superconnection involving a bi-fundamental scalar field which corresponds to the open-string tachyon of brane-antibrane configurations and which is naturally identified with the holographic dual of the quark condensate in chiral symmetry breaking. This realizes both the axial and chiral anomalies of QCD with a Witten-Veneziano mechanism for the $\eta'$ mass in addition to current quark masses, but somewhat differently than in the Katz-Schwartz AdS/QCD model used previously by us to evaluate pseudoscalar and axial vector transition form factors and their contribution to the HLBL piece of the muon $g-2$. Compared to the Katz-Schwartz model, we obtain a significantly more realistic description of axial-vector mesons with regard to $f_1$-$f_1'$ mixing and equivalent photon rates. Moreover, predictions of the $f_1\to e^+e^-$ branching ratios are found to be in line with a recent phenomenological study. However, pseudoscalar transition form factors compare less well with experiment; in particular the $\pi^0$ transition form factor turns out to be overestimated at moderate non-zero virtuality. For the combined HLBL contribution to the muon $g-2$ from the towers of axial vector mesons and excited pseudoscalars we obtain, however, a result very close to that of the Katz-Schwartz model.