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

We calculate the structure function $F_3(x,q^2)$ of the hadronic tensor of deep inelastic scattering (DIS) of charged leptons from glueballs of ${\cal {N}}=4$ 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 AdS$_5$ 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 $S^5$. 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.