We compute the electric dipole moment of nucleons in the large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f=2$ degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological $theta$ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result - a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be $d_n = 1.8 cdot 10^{-16}, theta;ecdot mathrm{cm}$. The electric dipole moment of the proton is exactly the opposite.
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