Shock Wave Collisions and Thermalization in AdS_5

Abstract

We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS_5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS_5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.

10 pages, 6 figures, based on talks given at the Symposium on High Energy Strong Interactions 2010 (HESI 2010), Yukawa Institute for Theoretical Physics, Kyoto, Japan, August 9-13, 2010, and at the 4th International Conference on Hard and Electromagnetic Probes of High Energy Nuclear Collisions (Hard Probes 2010), Eilat, Israel, October 10-15, 2010

References in corpus (9)

• Large N Field Theories, String Theory and Gravity
• Classical Black Hole Production in High-Energy Collisions
• Gluon Production at High Transverse Momentum in the McLerran-Venugopalan Model of Nuclear Structure Functions
• Asymptotic perfect fluid dynamics as a consequence of AdS/CFT
• Entropy production in collisions of gravitational shock waves and of heavy ions
• On the collision of two shock waves in AdS5
• Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision
• Off-center collisions in AdS_5 with applications to multiplicity estimates in heavy-ion collisions
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• Holographic Thermalization from Kerr-AdS
• Holographic dual of collimated radiation
• $q\bar{q}$ Potential at Finite T and Weak Coupling in $\mathcal{N}=4$