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Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

Ram Brustein1,2,* and A. J. M. Medved3,4,†

  • 1Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel
  • 2CERN, Theory Division, CH-1211, Geneva 23, Switzerland
  • 3Department of Physics & Electronics, Rhodes University, Grahamstown 6140 South Africa
  • 4School of Physics, KIAS, Dongdaemun-gu, Seoul 130-722, Korea

  • *ramyb@bgu.ac.il,
  • †j.medved@ru.ac.za
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Phys. Rev. D 83, 126005 – Published 8 June, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.126005

Abstract

We discuss corrections to the ratio of shear viscosity to entropy density η/s in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio η/s remains at the Einstein-gravity value of 1/4π to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, η/s can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of η/s can decrease below 1/4π when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein gravity.

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Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in ultraviolet-complete theories with a gravity dual

Ram Brustein and A. J. M. Medved
Phys. Rev. D 84, 126005 (2011)

Article Text

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Phys. Rev. D 83, 126005– Published 8 June, 2011
  • Received 19 October 2010

© 2011 American Physical Society

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