Early Time Dynamics in Heavy Ion Collisions from AdS/CFT Correspondence

TL;DR

The paper studies the onset of isotropization in a strongly coupled quark-gluon plasma using AdS/CFT in a Bjorken flow setup. By applying holographic renormalization and enforcing a real, single-valued bulk metric, it derives an early-time regime with constant energy density and negative longitudinal pressure, and recovers late-time Bjorken hydrodynamics with $\epsilon(\tau) \sim \tau^{-4/3}$. Matching the two regimes yields an estimate of the isotropization time, $\tau_{\text{iso}} \approx 0.3$ fm/c for RHIC kinematics, in line with hydrodynamic simulations. The work thus demonstrates a continuous, strongly coupled transition from an initially anisotropic state to an isotropic, hydrodynamic evolution.

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 we show that Bjorken hydrodynamics solution, obtained recently by Janik and Peschanski using gauge-gravity duality [hep-th/0512162], 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 similar strategy to show that the energy density approaches a constant as proper time goes to zero. 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 0.3 fm/c, in good agreement with results of hydrodynamic simulations.

Figures (2)

• Figure 1: The locations of branching points $z_c^\text{early}$ and $z_c^\text{late}$ for the early- and late-time metrics in the $z, \tau$-plane. The intersection of the two curves gives our estimate of the isotropization time $\tau_\text{iso}$ (see text).
• Figure 2: The scaling of energy density $\epsilon$ with proper time $\tau$ in heavy ion collisions for a strongly-coupled system as described by AdS/CFT correspondence. At late time Bjorken hydrodynamics is recovered, as was shown in Janik:2005zt. At early times the energy density goes to a constant, as shown in this work. Our estimate of the isotropization time $\tau_\text{iso}$ is likely located in some transition (isotropization) region.