DIS off glueballs from string theory: the role of the chiral anomaly and the Chern-Simons term

We calculate the structure function F3(x, q2) of the hadronic tensor of deep inelastic scattering (DIS) of charged leptons from glueballs of $$ \mathcal{N}=4 $$ SYM theory at strong coupling and at small values of the Bjorken parameter in the gauge/string theory duality framework. This is done in terms of type IIB superstring theory scattering amplitudes. From the AdS5 perspective, the relevant part of the scattering amplitude comes from the five-dimensional non-Abelian Chern-Simons terms in the SU(4) gauged supergravity obtained from dimensional reduction on S5. From type IIB superstring theory we derive an effective Lagrangian describing the four-point interaction in the local approximation. The exponentially small regime of the Bjorken parameter is investigated using Pomeron techniques.