Thermalization of Strongly Coupled Field Theories

V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri, B. Müller, A. Schäfer, M. Shigemori, and W. Staessens

Phys. Rev. Lett. 106, 191601 – Published 9 May 2011

Abstract

Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in $d = 2$ , 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.

Received 28 January 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.191601

Authors & Affiliations

V. Balasubramanian¹, A. Bernamonti², J. de Boer³, N. Copland², B. Craps², E. Keski-Vakkuri⁴, B. Müller⁵, A. Schäfer⁶, M. Shigemori⁷, and W. Staessens²

¹David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
²Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay Institutes, B-1050 Brussels, Belgium
³Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam, The Netherlands
⁴Helsinki Institute of Physics and Department of Physics, FIN-00014 University of Helsinki, Finland
⁵Department of Physics and CTMS, Duke University, Durham, North Carolina 27708, USA
⁶Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
⁷Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602, Japan