The analytical treatment of the nonperturbative QCD dynamics is one of main open questions of the strong interactions. Currently, it is only possible to get some qualitative information about this regime considering other QCD-like theories, as for ex
ample the N=4 super Yang-Mills (SYM), where one can perform calculations in the nonperturbative limit of large t Hooft coupling using the Anti-de Sitter space/Conformal field theory (AdS/CFT). Recently, the high energy scattering amplitude was calculated in the AdS/CFT approach, applied to deep inelastic scattering (DIS) and confronted with the $F_2$ HERA data. In this work we extend the nonperturbative AdS/CFT inspired model for diffractive processes and compare its predictions with a perturbative approach based on the Balitsky - Kovchegov (BK) equation. We demonstrate that the AdS/CFT inspired model is not able to describe the current $F_2^{D(3)}$ HERA data and predicts a similar behavior to that from BK equation in the range $10^{-7} lesssim x_{IP} lesssim 10^{-4}$. At smaller values of $x_{IP}$ the diffractive structure function is predicted to be energy independent.
The perturbative QCD predicts that the growth of the gluon density at small-$x$ (high energies) should saturate, forming a Color Glass Condensate (CGC), which is described in mean field approximation by the Balitsky-Kovchegov (BK) equation. Recently,
the next-to-leading order corrections for the BK equation were derived and a global fit of the inclusive $ep$ HERA data was performed, resulting in a parameterization for the forward scattering amplitude. In this paper we compare this parameterization with the predictions of other phenomenological models and investigate the saturation physics in diffractive deep inelastic electron-proton scattering and in the forward hadron production in $pp$ collisions. Our results demonstrate that the running coupling BK solution is able to describe these observables.
