Holographic thermalization in a top-down confining model

Abstract

It is interesting to ask how a confinement scale affects the thermalization of strongly coupled gauge theories with gravity duals. We study this question for the AdS soliton model, which underlies top-down holographic models for Yang-Mills theory and QCD. Injecting energy via a homogeneous massless scalar source that is briefly turned on, our fully backreacted numerical analysis finds two regimes. Either a black brane forms, possibly after one or more bounces, after which the pressure components relax according to the lowest quasinormal mode. Or the scalar shell keeps scattering, in which case the pressure components oscillate and undergo modulation on time scales independent of the (small) shell amplitude. We show analytically that the scattering shell cannot relax to a homogeneous equilibrium state, and explain the modulation as due to a near-resonance between a normal mode frequency of the metric and the frequency with which the scalar shell oscillates.

Thermalization of Wightman functions in AdS/CFT and quasinormal modes

“…The time scale at which a given quantity approaches the value that it takes in a thermal state (with temperature determined by the energy of the initial nonequilibrium state) is called the thermalization time associated with the observable. In many situations, in the context of holography, it has been found that expectation values of local operators, which we will call one-point functions, approach their thermal values with rates dictated by the lowest quasinormal mode of the corresponding bulk field (see [1,2] for two examples demonstrating this point). Phrased in field theory language, the time scale on which one-point functions thermalize, starting from a far-from-equilibrium state, is the same on which infinitesimally small perturbations away from thermal equilibrium decay back to equilibrium.…”

“…The computation of this quantity requires the knowledge of the Wightman two-point function. 2 The definition was inspired by the fluctuation dissipation relation in a thermal state and has already been used earlier in the context of nonequilibrium quantum field theory (see e.g. [15]).…”

Confining D-instanton background in an external electric field

“…Recently there has been a growing interest in studying the quantum quenches in the confined phase (see e.g. [30][31][32]), where they have found some evidence that the equilibrium (formation of a black hole in the gravity side) may not be the final fate of a system driven far from equilibrium by applying a quench. In this regard, it would be interesting to study the evolution of a confining theory like the one in the present paper under electric field quenches, as an important class of quenches.…”

Thermalization and confinement in strongly coupled gauge theories

“…This process appears to repeat for as long as the numerical routines of [5] were able to run. Recently, analogous calculations were performed in the AdS soliton background [6] which is qualitatively similar to the hardwall in that there is a mass gap for black brane formation in the bulk. There too perturbations were identified which appear to scatter indefinitely, while others lead to collapse and black-brane formation.…”