Early time dynamics in heavy-ion collisions from AdS/CFT correspondence

Abstract

We study the matter produced in heavy-ion collisions, assuming that this matter is strongly interacting and employing AdS/CFT correspondence to investigate its dynamics. At late proper times \ensuremath{\tau} we show that Bjorken hydrodynamics solution, obtained recently by Janik and Peschanski using gauge-gravity duality [1], can be singled out by simply requiring that the metric tensor is a real and single-valued function of the coordinates everywhere in the bulk, without imposing any constraints on the curvature invariant. At early proper times we use a similar strategy to show that the energy density $\ensuremath{\epsilon}$ approaches a constant as $\ensuremath{\tau}\ensuremath{\rightarrow}0$. We therefore demonstrate that the strong coupling dynamics incorporates the isotropization transition in heavy-ion collisions. By matching our early-time regime with the late-time one of Janik and Peschanski we estimate the isotropization time at RHIC to be approximately ${\ensuremath{\tau}}_{\mathrm{iso}}\ensuremath{\approx}0.3$ fm/$c$, in good agreement with results of hydrodynamic simulations.