Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators

TL;DR

This paper models gauge theory thermalization via a collapsing shell in AdS space, analyzing the evolution of correlator singularities, revealing a decrease in singularities indicating decoherence, and exploring complex singularities from normal and quasi-normal modes.

Contribution

It introduces a dynamic shell moving at finite velocity in AdS, extending previous quasi-static models, and analyzes the evolution of correlator singularities during thermalization.

Findings

Number of singularities decreases to zero as thermalization progresses.

Singularities in the complex time plane are characterized by normal and quasi-normal modes.

The decrease in singularities suggests a decoherence process during thermalization.

Abstract

We consider a gauge/gravity dual model of thermalization which consists of a collapsing thin matter shell in asymptotically Anti-de Sitter space. A central aspect of our model is to consider a shell moving at finite velocity as determined by its equation of motion, rather than a quasi-static approximation as considered previously in the literature. By applying a divergence matching method, we obtain the evolution of singularities in the retarded unequal time correlator $G^R(t,t')$, which probes different stages of the thermalization. We find that the number of singularities decreases from a finite number to zero as the gauge theory thermalizes. This may be interpreted as a sign of decoherence. Moreover, in a second part of the paper, we show explicitly that the thermal correlator is characterized by the existence of singularities in the complex time plane. By studying a quasi-static state, we show the singularities at real times originate from contributions of normal modes. We also investigate the possibility of obtaining complex singularities from contributions of quasi-normal modes.