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We study the anomalous electromagnetic pion form factor$F_{\pi^0\gamma^*\gamma^*}$ with a set of holographic models. By comparing withthe 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 quadraticslope parameters of $F_{\pi^0\gamma^*\gamma^*}$, currently out of experimentalreach but testable in the near future. We find it particularly useful to encodethis low-energy information in a form factor able to satisfy also QCDshort-distance constraints. We choose the form factor introduced by D'Ambrosio,Isidori and Portoles in kaon decays, which has the right short distance for aparticular value of the quadratic slope, which is later shown to be compatiblewith our holographic predictions. We then turn to a determination of the(dominant) pion exchange diagram in the hadronic light by light scatteringcontribution to the muon anomalous magnetic moment. We quantify the theoreticaluncertainty in $(g-2)_{\mu}$ coming from the different input we use: QCD shortdistances, experimental input and low-energy holographic predictions. We alsotest the pion-pole approximation. Our final result is$a_{\mu}^{\pi^0}=6.54(25)\cdot 10^{-10}$, where the error is driven by thelinear slope of $F_{\pi^0\gamma^*\gamma^*}$, soon to be measured with precisionat KLOE-2. Our numerical analysis also indicates that large values of themagnetic susceptibility $\chi_0$ are disfavored, therefore pointing at a mildeffect from the pion off-shellness. However, in the absence of stronger boundson $\chi_0$, an additional $(10-15)%$ systematic uncertainty on the previousvalue for $a_\mu^{\pi^0}$ cannot be excluded.

The hadronic light by light contribution to the $(g-2)_{\mu}$ with holographic models of QCD