Boost-invariant early time dynamics from AdS/CFT

TL;DR

This paper investigates the early-time boost-invariant dynamics of a strongly-coupled conformal plasma using AdS/CFT, revealing the dependence on initial conditions, the absence of a scaling solution, and insights into thermalization.

Contribution

It provides the first analysis of early-time dynamics in boost-invariant AdS/CFT, highlighting the role of initial conditions and the non-existence of a scaling solution.

Findings

No early-time scaling solution exists.

Boundary dynamics depend on initial conditions.

Transition to hydrodynamics observed via resummation.

Abstract

Boost-invariant dynamics of a strongly-coupled conformal plasma is studied in the regime of early proper-time using the AdS/CFT correspondence. It is shown, in contrast with the late-time expansion, that a scaling solution does not exist. The boundary dynamics in this regime depends on initial conditions encoded in the bulk behavior of a Fefferman-Graham metric coefficient at initial proper-time. The relation between the early-time expansion of the energy density and initial conditions in the bulk of AdS is provided. As a general result it is proven that a singularity of some metric coefficient in Fefferman-Graham frame exists at all times. Requiring that this singularity at tau = 0 is a mere coordinate singularity without the curvature blow-up gives constraints on the possible boundary dynamics. Using a simple Pade resummation for solutions satisfying the regularity constraint, the features of a transition to local equilibrium, and thus to the hydrodynamical late-time regime, have been observed. The impact of this study on the problem of thermalization is discussed.