Thermalization of Wightman functions in AdS/CFT and quasinormal modes

TL;DR

This paper investigates how two-point functions in a holographic setup thermalize after a quench, showing that the lowest quasinormal mode governs the thermalization rate, with implications for higher-dimensional spacetimes.

Contribution

It demonstrates that the thermalization of Wightman functions in AdS/CFT is controlled by the lowest quasinormal mode, providing a heuristic for general Vaidya spacetimes.

Findings

Wightman functions thermalize at a rate set by the lowest quasinormal mode.

Effective occupation numbers approach the thermal Bose-Einstein distribution.

Comparison with geodesic approximation highlights differences in thermalization dynamics.

Abstract

We study the time evolution of Wightman two-point functions of scalar fields in AdS$_3$-Vaidya, a spacetime undergoing gravitational collapse. In the boundary field theory, the collapse corresponds to a quench process where the dual 1+1 dimensional CFT is taken out of equilibrium and subsequently thermalizes. From the two-point function, we extract an effective occupation number in the boundary theory and study how it approaches the thermal Bose-Einstein distribution. We find that the Wightman functions, as well as the effective occupation numbers, thermalize with a rate set by the lowest quasinormal mode of the scalar field in the BTZ black hole background. We give a heuristic argument for the quasinormal decay, which is expected to apply to more general Vaidya spacetimes also in higher dimensions. This suggests a unified picture in which thermalization times of one- and two-point functions are determined by the lowest quasinormal mode. Finally, we study how these results compare to previous calculations of two-point functions based on the geodesic approximation.