  We study the anomalous electromagnetic pion form factor
$F_{\pi^0\gamma^*\gamma^*}$ with a set of holographic models. By comparing with
the measured value of the linear slope, some of these models can be ruled out.
From the remaining models we obtain predictions for the low-energy quadratic
slope parameters of $F_{\pi^0\gamma^*\gamma^*}$, currently out of experimental
reach but testable in the near future. We find it particularly useful to encode
this low-energy information in a form factor able to satisfy also QCD
short-distance constraints. We choose the form factor introduced by D'Ambrosio,
Isidori and Portoles in kaon decays, which has the right short distance for a
particular value of the quadratic slope, which is later shown to be compatible
with our holographic predictions. We then turn to a determination of the
(dominant) pion exchange diagram in the hadronic light by light scattering
contribution to the muon anomalous magnetic moment. We quantify the theoretical
uncertainty in $(g-2)_{\mu}$ coming from the different input we use: QCD short
distances, experimental input and low-energy holographic predictions. We also
test the pion-pole approximation. Our final result is
$a_{\mu}^{\pi^0}=6.54(25)\cdot 10^{-10}$, where the error is driven by the
linear slope of $F_{\pi^0\gamma^*\gamma^*}$, soon to be measured with precision
at KLOE-2. Our numerical analysis also indicates that large values of the
magnetic susceptibility $\chi_0$ are disfavored, therefore pointing at a mild
effect from the pion off-shellness. However, in the absence of stronger bounds
on $\chi_0$, an additional $(10-15)%$ systematic uncertainty on the previous
value for $a_\mu^{\pi^0}$ cannot be excluded.
