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We study the deep inelastic scattering (DIS) of a proton-targeted lepton inthe presence of gluon condensation using gauge/gravity duality. We use amodified $AdS_5$ background where the modification parameter $c$ corresponds tothe gluon condensation in the boundary theory. Firstly, when examining theelectromagnetic field, we find that non-zero $c$ can increase the magnitude ofthe field. Our goal is to find the acceptable value of $c$ for this scatteringand our method is based on setting the mass of the proton as an eigenvalue ofthe baryonic state equations of the DIS to find the acceptable value of theparameter c on the other side of the equations. Therefore in the second step,we calculate wave function equations for the baryonic states where the mass ofthe proton target requires a value contribution of $c$ as $c = 0.0120 {\rmGeV}^4$. Proceeding by the electromagnetic field and the baryonic states, wederive the holographic interaction action related to the amplitude of thescattering. Finally, we compute the corresponding structure functionsnumerically as functions of $x$ and $q$, which are Bjorken variables and thelepton momentum transfers, respectively. Comparing the Jlab Hall $C$ data withour theoretical calculations, our results are acceptable.

Deep inelastic scattering with proton target in the presence of gluon condensation using holography