HET journal club: Ayan Mukhopadhyay (E.Polytechnique / Saclay) – Niels Bohr Institute - University of Copenhagen

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HET journal club: Ayan Mukhopadhyay (E.Polytechnique / Saclay)

Emergence of spacetimes dual to fluids and the holographic RG flow

We show how spacetimes of the fluid/gravity correspondence can be constructed from the holographic fluid RG flow. This RG flow is evolution of hydrodynamic data on holographic screens which give a hypersurface foliation of the spacetime. It is a system of first order ordinary differential equations which can be obtained directly from Einstein's equations without any explicit knowledge of the metric. This requires the choice of Fefferman-Graham foliation when the cosmological constant is negative. Solving this RG flow is equivalent to explicitly solving for the metric. This RG flow can be uniquely solved by requiring finiteness of horizon transport coefficients. The near horizon forms of these transport coefficients can be fixed independently of their boundary values, which are traditionally determined from the explicit metric. Our results suggest that all counterterms can be uniquely specified by requiring finiteness of horizon transport coefficients as well. It supports our conjecture that the general holographic RG flow has no scheme dependence aside from a trivial re-parameterization of the scale and can be determined uniquely from the hydrodynamic limit. Furthermore, the asymptotic data can be reconstructed from RG flow by imposing appropriate conditions on the data of the infrared holographic screen where Fefferman-Graham foliation terminates. Explicit calculations up to second order in derivative expansion suggest that the (infrared) horizon fluid is incompressible Navier-Stokes forced by the curvature of the metric only.