We discuss unpolarized neutrino- and anti-neutrino-nucleon deep inelastic scattering (DIS) using a chiral doublet of baryonic sources with explicit symmetry breaking, in a slice of AdS$_5$ with both a hard and soft wall. We explicitly derive the direct and transition form factors for the vector and axial-vector currents for the holographic dual of a proton and neutron. We use them to derive the s-channel structure functions for neutrino and anti-neutrino scattering on a proton and neutron in bulk. The t-channel contributions stemming from the Pomeron and Reggeon exchanges are also evaluated explicitly. The pertinent even and odd structure functions in the limit of large and small parton momentum fraction $x$ are given. The results allow for the extraction of the nonperterbative parton distribution functions carried by the sea and valence quarks both at large-x and small-x regimes. Our holographic PDF sets compare well with LHAPDF and CTEQ PDF sets in the large-x and small-x regimes in the intermediate range of $Q^2<10~rm{GeV^2}$.
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