We try to understand the recently observed anomalous behavior of the
photon-to-pion transition form factor in the holographic QCD approach. First
the holographic description of the anomalous \gamma^*\gamma^*\pi^0 form factor
is reviewed and applied to various models. It is illustrated that in describing
the anomalous form factor, the holographic approach is asymptotically dual to
the perturbative QCD (pQCD) framework, with the pion mode \pi(z)\sim z
corresponding to the asymptotic pion distribution amplitude. This indicates
some inconsistency in light-front holography, since \pi(z)\sim z would be dual
to \varphi(x)\sim \sqrt{x(1-x)} there. After clarifying these subtleties, we
employ the relation between the holographic and the perturbative expressions to
study possible asymptotic violation of the transition form factor. It is found
that if one require that the asymptotic form factor possess a pQCD-like
expression, the pion mode can only be ultraviolet-enhanced by logarithmic
factors. The minimally deformed pion mode will then be of the form \pi(z)\sim
z\ln (z\Lambda)^{-1}. We suppose that this deformation may be due to the
coupling of the pion with a nontrivial open string tachyon field, and then the
parameter Λ will be related to the quark condensate. Interestingly,
this pion mode leads immediately to Radyushkin's logarithmic model, which
fitted very well the experimental data in the large-Q^2 region. On the other
side, the pQCD interpretation with a flat-like pion distribution amplitude,
proposed by Radyushkin and Polyakov, fails to possess a holographic expression.Comment: a few typos corrected, references added, version published in EPJ