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All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence · Around

2014

All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence

Bu, Yanyan, Lublinsky, Michael

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Using fluid/gravity correspondence, we determine the (linearized) stress energy tensor of $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling with all orders in derivatives of fluid velocity included.

We find that the dissipative effects are fully encoded in the shear term and a new one, which emerges starting from the third order.
We derive, for the first time, closed linear holographic RG flow-type equations for (generalized) momenta-dependent viscosity functions.
In the hydrodynamic regime, we obtain the stress tensor up to third order in derivative expansion analytically.

Built on

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P. Kovtun and A. Starinets, “Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory,” Phys.Rev.Lett
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2007
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M. Lublinsky and E. Shuryak, “How much entropy is produced in strongly coupled Quark-Gluon Plasma (sQGP) by dissipative effects?,” Phys.Rev
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S. Bhattacharyya, V. E. Hubeny, S. Minwalla, and M. Rangamani, “Nonlinear Fluid Dynamics from Gravity,” JHEP
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Then

M. Lublinsky and E. Shuryak, “Improved Hydrodynamics from the AdS/CFT,” Phys.Rev
Original
2009
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S. Bhattacharyya, R. Loganayagam, S. Minwalla, S. Nampuri, S. P. Trivedi, et al
Original
2009
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N. Iqbal and H. Liu, “Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm,” Phys.Rev
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2009
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M. Lublinsky and E. Shuryak, “Universal hydrodynamics and charged hadron multiplicity at the LHC,” Phys.Rev
Original
2011
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M. P. Heller, R. A. Janik, and P. Witaszczyk, “The characteristics of thermalization of boost-invariant plasma from holography,” Phys.Rev.Lett

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Y. Bu and M. Lublinsky, work in preparation

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