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

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