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 -