Wilsonian Approach to Fluid/Gravity Duality
| Title: | Wilsonian Approach to Fluid/Gravity Duality |
| Author: |
Keeler, Cynthia; Bredberg, Irene; Lysov, Vyacheslav; Strominger, Andrew E.
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | Bredberg, Irene, Cynthia Keeler, Vyacheslav Lysov, and Andrew E. Strominger. 2011. Wilsonian approach to fluid/gravity duality. Journal of High Energy Physics 2011(3): 141. |
| Full Text & Related Files: |
1006.1902v2.pdf (326.7Kb; PDF) 
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| Abstract: | The problem of gravitational fluctuations confined inside a finite cutoff at radius \(r=r_c\) outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff \(r_c\) the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant \(D(r_c)\) is derived. The dependence on \(r_c\) is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for \(D(\infty)\) reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant \(D(horizon)\) reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio \(\frac{\eta} {s}\) is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included. |
| Published Version: | doi:10.1007/JHEP03(2011)141 |
| Other Sources: | http://arxiv.org/abs/1006.1902 |
| Terms of Use: | This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:8156523 |
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