Universal hydrodynamics of non-conformal branes

By Ingmar Kanitscheider, Kostas Skenderis. 2009

221 citations recorded by the source corpus.

We examine the hydrodynamic limit of non-conformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to non-conformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of non-conformal branes is fully determined in terms of conformal hydrodynamics. Using previous results on the latter we predict the form of the non-conformal hydrodynamic stress tensor to second order in derivatives. Furthermore we show that the ratio between bulk and shear viscosity is fixed by the generalized conformal structure to be ζ/η = 2(1/(d−1)−cs2), where cs is the speed of sound in the fluid.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/93ad6f0749e76c0c22799f43f748cc2d4f3bee1f

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Citations in the corpus

Adiabatic hydrodynamics: the eightfold way to dissipation (2015, background): “Another direction to consider is neutral fluids without Weyl invariance, but since the simplest set-ups realizable holographically secretly enjoy higher dimensional conformal invariance [102] (see also [103, 104]) it is easy to intuit that these analyses won’t provide more detailed insight (see howe”
Relativistic Fluid Dynamics in and out of Equilibrium (2017, unknown): “[54, 140, 141] [119, 120, 142] [67, 130, 143] [144–146] [147]”
Quantum critical lines in holographic phases with (un)broken symmetry (2012, methodology): “In section 4, we shall also reinterpret the scaling properties of such hyperscaling violating solutions in terms of generalized dimensional reduction, which involves the analytic continuation of the number of reduced dimensions, and see how they may be connected to hyperscaling solutions, [23, 5, 24”
Weak Field Black Hole Formation in Asymptotically AdS Spacetimes (2009, methodology): “responding spacetime is locally (tube wise) well described by a black brane metric with a value of the temprature that varies with ~x(see (5.1) and the discusson arounf it in section 5). According to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], the subsequent evolution of”
Relativistic viscous fluid dynamics and non-equilibrium entropy (2009, methodology): “). This serves as another consistencycheck of the above approach. It would be interesting to calculate the entropy current from the black hole horizon corresponding to the geometry considered in Ref. [26] and check that its form fulﬁlls the conditions on B1,B3,B4,B5,B6,A2,A3,A5 found in section 4.2.”
Improved Holographic QCD (2010, background): “This bound is trivially satisfied for exact conformal theories such as N = 4 YM, and saturated in theories on Dp branes [78, 79].”
Gauge/String Duality, Hot QCD and Heavy Ion Collisions (2011, background): “As for the case of the bulk viscosity, the variable ( 1 3 − c 2 s ) can be used to parametrize deviations from conformality, and all transport coefficients can indeed be written explicitly as functions of ( 1 3 − c 2 s ) [435].”
Thermal transport and drag force in improved holographic QCD (2009, background): “t the bound is proposed to hold in the entire range of temperature from Tc to ∞. This bound is trivially satisﬁed for exact conformal theories such as N = 4 YM, and saturated in theories on Dp branes [57, 58]. With the numerical evaluation at hand, we can check (3.25) in our case. In ﬁgure 8 (a) we ”
The fluid/gravity correspondence: a new perspective on the membrane paradigm (2010, unknown): “[53, 54] as well as to non-relativistic fluids [55, 56], which allows us to make closer contact with familiar everyday systems.”
Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, background): “While all these discussions are for conformal fluids whose duals are asymptotically AdS spacetimes, one can extend the discussion to non-conformal fluids living on Dp-brane worldvolumes [77, 78] as well as explorations involving higher derivative terms in the gravitational description [79].”