## Abstract

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.

Original language | American English |
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Article number | 126005 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 84 |

Issue number | 12 |

DOIs | |

State | Published - 7 Dec 2011 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)