CFT dual of the AdS Dirichlet problem: fluid/gravity on cut-off surfaces

被引:51
作者
Brattan, Daniel [1 ,2 ]
Camps, Joan [1 ,2 ]
Loganayagam, R. [3 ]
Rangamani, Mukund [1 ,2 ]
机构
[1] Univ Durham, Ctr Particle Theory, Durham DH1 3LE, England
[2] Univ Durham, Dept Math Sci, Sci Labs, Durham DH1 3LE, England
[3] Harvard Univ, Harvard Soc Fellows, Cambridge, MA 02138 USA
关键词
Gauge-gravity correspondence; AdS-CFT Correspondence; Black Holes; Holography and condensed matter physics (AdS/CMT);
D O I
10.1007/JHEP12(2011)090
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one can determine non-linear solutions to this problem in the long wavelength regime. On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a 'dynamical' background metric which depends on the local fluid velocities and temperature. This boundary fluid can be re-expressed as an emergent hypersurface fluid which is non-conformal but has the same value of the shear viscosity as the boundary fluid. The hypersurface dynamics arises as a collective effect, wherein effects of the background are transmuted into the fluid degrees of freedom. Furthermore, we demonstrate that this collective fluid is forced to be non-relativistic below a critical cut-off radius in AdS to avoid acausal sound propagation with respect to the hypersurface metric. We further go on to show how one can use this set-up to embed the recent constructions of flat spacetime duals to non-relativistic fluid dynamics into the AdS/CFT correspondence, arguing that a version of the membrane paradigm arises naturally when the boundary fluid lives on a background Galilean manifold.
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页数:74
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