Thermalization of Wightman functions in AdS/CFT and quasinormal modes

Ville Keränen and Philipp Kleinert
Phys. Rev. D 94, 026010 – Published 28 July 2016

Abstract

We study the time evolution of Wightman two-point functions of scalar fields in AdS3-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.

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  • Received 14 January 2016

DOI:https://doi.org/10.1103/PhysRevD.94.026010

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Ville Keränen* and Philipp Kleinert

  • Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom

  • *vkeranen1@gmail.com
  • philipp.kleinert@physics.ox.ac.uk

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Issue

Vol. 94, Iss. 2 — 15 July 2016

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