Entanglement in Reggeized Scattering using AdS/CFT

The eikonalized parton-parton scattering amplitude at large $\sqrt{s}$ and large impact parameter, is dominated by the exchange of a hyperbolic surface in walled AdS. Its analytical continuation yields a worldsheet instanton that is at the origin of the Reggeization of the amplitude and a thermal-like quantum entropy ${\cal S}_T$. We explicitly construct the entangled density matrix following from the exchanged surface, and show that its von-Neumann entanglement entropy ${\cal S}_E$ coincides with the thermal-like entropy, i.e. ${\cal S}_T={\cal S}_E$. The ratio of the entanglement entropy to the transverse growth of the exchanged surface is similar to the Bekenstein entropy ratio for a black-hole, with a natural definition of saturation and the on-set of chaos in high energy collisions. The largest eigenvalues of the entangled density matrix obey a cascade equation in rapidity, reminiscent of non-linear QCD evolution of wee-dipoles at low-x and weak coupling. We suggest that the largest eigenvalues describe the probability distributions of wee-quanta at low-x and strong coupling that maybe measurable at present and future pp and ep colliders.