Holographic approach to thermalization in general anisotropic theories

TL;DR

This paper uses holography to analyze how strongly-coupled anisotropic field theories thermalize after a quench, by calculating entanglement entropy growth in various anisotropic geometries.

Contribution

It extends holographic thermalization studies to general anisotropic scalings, including Lifshitz and hyperscaling violating fixed points, with new calculations of entanglement entropy evolution.

Findings

Entanglement entropy growth characterizes thermalization rate.

Constraints on scaling parameters from energy conditions and extremal surface existence.

Results applicable for experimental comparison and other thermalization probes.

Abstract

We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a Vaidya-like time-dependent geometry where the asymptotic metric has general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal surface and use it to calculate the time-dependent entanglement entropy between a strip region with width $2R$ and its outside region. In the special case with an isotropic metric, we also explore the entanglement entropy for a spherical region of radius $R$. The growth of the entanglement entropy characterizes the thermalization rate after a quench. We study the thermalization process in the early times and late times in both large $R$ and small $R$ limits. The allowed scaling parameter regions are constrained by the null energy conditions as well as the condition for the existence of the Ryu-Takanayagi extremal surfaces. This generalizes the previous works on this subject. All obtained results can be compared with experiments and other methods of probing thermalization.