Thermalization in a Holographic Confining Gauge Theory

TL;DR

This paper investigates how a confining gauge theory thermalizes after time-dependent perturbations by analyzing the dual gravitational Einstein-dilaton model, revealing that thermalization times are governed by quasi-normal modes and identifying universal scaling behaviors.

Contribution

It introduces a detailed analysis of thermalization dynamics in a holographic confining gauge theory, linking thermalization times to quasi-normal modes and exploring universal scaling in abrupt quenches.

Findings

Thermalization time is set by the imaginary part of the lowest quasi-normal mode.

The final state depends on quench parameters and exhibits a dynamical phase diagram.

Universal scaling behavior is observed in the abrupt quench limit.

Abstract

Time dependent perturbations of states in the holographic dual of a 3+1 dimensional confining theory are considered. The perturbations are induced by varying the coupling to the theory's most relevant operator. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of motion subject to these boundary conditions. We compute the characteristic time scale of many thermalization processes, noting that in every case we examine, this time scale is determined by the imaginary part of the lowest lying quasi-normal mode of the final state black brane. We quantify the dependence of this final state on parameters of the quench, and construct a dynamical phase diagram. Further support for a universal scaling regime in the abrupt quench limit is provided.