TY - JOUR

T1 - Proof of a universal lower bound on the shear viscosity to entropy density ratio

AU - Brustein, Ram

AU - Medved, A. J.M.

N1 - Funding Information:
We thank Ofer Aharony, Alex Buchel and particularly Rob Myers and Aninda Sinha for discussions. The research of RB was supported by The Israel Science Foundation grant no 470/06 . The research of AJMM is supported by the University of Seoul. AJMM thanks Ben-Gurion University for their hospitality during his visit.

PY - 2010/7/1

Y1 - 2010/7/1

N2 - It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4Π in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.

AB - It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4Π in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.

KW - Black branes

KW - Gauge/gravity duality

KW - Generalized gravity

KW - Hydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=77954141799&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2010.06.018

DO - 10.1016/j.physletb.2010.06.018

M3 - Article

AN - SCOPUS:77954141799

SN - 0370-2693

VL - 691

SP - 87

EP - 90

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 2

ER -