Deep Inelastic Scattering from the AdS/CFT correspondence

Abstract

We calculate the cross section of an ultra relativistic nucleus scattering on a qq^(bar) pair at large coupling in N=4 SUSY gauge theory. We study the problem in the context of the AdS/CFT correspondence. The nucleus is modeled as a gravitational shockwave in an AdS_5 background moving along the light cone. The dipole qq^(bar) is represented by a Wilson loop moving in the opposite direction. Due to the correspondence, calculating the scattering amplitude of the Wilson loop with the nucleus reduces to calculating the extreme value of the Nambu-Goto action for an open string. Its two end points are attached to the qq^(bar) respectively and it hangs in an AdS_5 shockwave spacetime. Six solutions are found two of which are physically meaningful. Both solutions predict that the saturation scale Q_s at high enough energies becomes energy independent; in particular it behaves as Q_s A^{1/3} where A is the atomic number. One solution predicts pomeron intercept alpha_p=2. However, there is a parameter window of r (dipole size) and s (c.m. energy) where it violates the black disk limit. On the other hand, the other solution respects this limit and corresponds to pomeron intercept alpha_p=1.5. We conjecture that this is the right value for gauge theories at strong coupling.