TY - JOUR

T1 - Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in ultraviolet-complete theories with a gravity dual

AU - Brustein, Ram

AU - Medved, A. J.M.

PY - 2011/12/7

Y1 - 2011/12/7

N2 - We reconsider, from a novel perspective, how unitarity constrains the corrections to the ratio of shear viscosity η to entropy density s. We start with higher-derivative extensions of Einstein gravity in asymptotically anti-de Sitter spacetimes. It is assumed that these theories are derived from string theory and thus have a unitary UV completion that is dual to a unitary, UV-complete boundary gauge theory. We then propose that the gravitational perturbations about a solution of the UV-complete theory are described by an effective theory whose linearized equations of motion have at most two time derivatives. Our proposal leads to a concrete prescription for the calculation of η/s for theories of gravity with arbitrary higher-derivative corrections. The resulting ratio can take on values above or below 1/4π and is consistent with all the previous calculations, even though our reasoning is substantially different. For the purpose of calculating η/s, our proposal also leads to only two possible candidates for the effective two-derivative theory: Einstein and Gauss-Bonnet gravity. The distinction between the two is that Einstein gravity satisfies the equivalence principle, and so its graviton correlation functions are polarization-independent, whereas the Gauss-Bonnet theory has polarization-dependent correlation functions. We discuss the graviton three-point functions in this context and explain how these can provide additional information on the value of η/s.

AB - We reconsider, from a novel perspective, how unitarity constrains the corrections to the ratio of shear viscosity η to entropy density s. We start with higher-derivative extensions of Einstein gravity in asymptotically anti-de Sitter spacetimes. It is assumed that these theories are derived from string theory and thus have a unitary UV completion that is dual to a unitary, UV-complete boundary gauge theory. We then propose that the gravitational perturbations about a solution of the UV-complete theory are described by an effective theory whose linearized equations of motion have at most two time derivatives. Our proposal leads to a concrete prescription for the calculation of η/s for theories of gravity with arbitrary higher-derivative corrections. The resulting ratio can take on values above or below 1/4π and is consistent with all the previous calculations, even though our reasoning is substantially different. For the purpose of calculating η/s, our proposal also leads to only two possible candidates for the effective two-derivative theory: Einstein and Gauss-Bonnet gravity. The distinction between the two is that Einstein gravity satisfies the equivalence principle, and so its graviton correlation functions are polarization-independent, whereas the Gauss-Bonnet theory has polarization-dependent correlation functions. We discuss the graviton three-point functions in this context and explain how these can provide additional information on the value of η/s.

UR - http://www.scopus.com/inward/record.url?scp=84855323095&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.84.126005

DO - 10.1103/PhysRevD.84.126005

M3 - Article

AN - SCOPUS:84855323095

VL - 84

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

M1 - 126005

ER -