Asymmetric Collision of Two Shock Waves in AdS_5

Abstract

We consider high energy collisions of two shock waves in AdS_5 as a model of ultrarelativistic nucleus-nucleus collisions in the boundary theory. We first calculate the graviton field produced in the collisions in the NLO and NNLO approximations, corresponding to three- and four-graviton exchanges with the shock waves. We then consider the asymmetric limit where the energy density in one shock wave is much higher than in the other one. In the boundary theory this setup corresponds to proton-nucleus collisions, with the nucleus being the denser of the two shock waves and the proton being the less dense one. Employing the eikonal approximation we find the exact high energy analytic solution for the metric in AdS_5 for the asymmetric collision of two delta-function shock waves. The solution resums all-order graviton exchanges with the "nucleus" shock wave and a single-graviton exchange with the "proton" shock wave. Using the holographic renormalization prescription we read off the energy-momentum tensor of the matter produced in proton-nucleus collisions. We show in explicit detail that in the boundary theory the proton is completely stopped by strong-coupling interactions with the nucleus, in agreement with our earlier results. We also apply the eikonal technique to the asymmetric collision of two unphysical delta-prime shock waves, which we introduced in an earlier work as a means of modeling nuclear collisions with weak coupling initial dynamics. We obtain a surprising result that, for delta-prime shock waves, the multiple bulk graviton exchange series giving the leading energy-dependent contribution to the energy-momentum tensor terminates at the order of two graviton exchanges with the nucleus.