Gravity and hydrodynamics: lectures on the fluid-gravity correspondence

Abstract

We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluid-gravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addition we also describe the recent developments extending the correspondence to incorporate matter fields and to non-relativistic systems. Based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge Theories, Geneva, Switzerland (February 2009). * mukund.rangamani@durham.ac.uk 1 In fact there are several results in the literature exploring the phase structure [12,13,14] and stability [15,16] of black holes using the dual fluid dynamics in the context of field theories compactified on spatial circles with supersymmetry breaking boundary conditions. These boundary conditions break conformal invariance and the field theories are confining in the infra-red.2 For recent developments on lattice computations see [17] and references therein.

Introductory lectures to large- QCD phenomenology and lattice results

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