Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm

By N. Iqbal, Hong Liu. 2008

648 citations recorded by the source corpus.

We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the ``membrane paradigm'' fluid of classical black hole mechanics. Thus, generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low-frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead, we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8f16848226ab6e6f35cd3e6152b24c00a9c532ff

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Citations in the corpus

Holographic Quantum Matter (2016, methodology): “We will follow a slightly modernized (in the spirit of [218]) version of the logic in [411], which in turn built on [478].”
Universal Resistivity from Holographic Massive Gravity (2013, methodology): “Our method follows the membrane paradigm approach of [17].”
Universal diffusion in incoherent black holes (2016, background): “This is because the charge susceptibility is also sensitive to the profile of the dilaton [36, 37] χ−1 = ∫ r0”
Momentum dissipation and effective theories of coherent and incoherent transport (2014, methodology): “More generally, adapting a procedure first described in [16], DC conductivities have been computed analytically, in a variety of models where momentum is not conserved, in terms of black brane horizon data [11, 15, 17–27].”
Novel metals and insulators from holography (2014, result): “This complements similar results for specific models in a translationally invariant context [36] and in the context of momentum dissipation [12, 25, 37].”
The thermoelectric properties of inhomogeneous holographic lattices (2014, background): “For the special case of the neutral AdS Schwarzschild black hole the second term in σ vanishes and the first term gives unity, and so we recover the result of [15].”
Real-time gauge/gravity duality: prescription, renormalization and examples (2008, background): “There have been several earlier works discussing holography in Lorentzian signature, including [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19].”
Wilsonian approach to fluid/gravity duality (2010, background): “7) will also apply to rc = ∞, in agreement with findings in [31,24].”
Real‐time response in AdS/CFT with application to spinors (2009, methodology): “The validity of these formulas even in real-time was a key element in the results relating AdS/CFT to the membrane paradigm in [10].”
Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, background): “One can of course use the AdS/CFT correspondence to interpolate between these two extreme descriptions [122]: if one so wishes, it is possible to define a fiducial membrane at some other radial location (and in particular on the stretched horizon) and identify the fluid dynamics on this surface.”
Brownian Motion in AdS/CFT (2008, neutral): “[49] argued that one can derive the universality of this ratio using the membrane paradigm, i.”
Holographic and Wilsonian renormalization groups (2010, background): “[36] gives an analysis of the flow between the horizon and the boundary that is similar in form to our discussion of domain wall flow.”
From Navier-Stokes to Einstein (2011, result): “Although far from obvious at first glance, these results from AdS/CFT are compatible with, and in some cases equivalent to, the earlier results from pure gravity [10,23,28,52,53].”
Gauge/String Duality, Hot QCD and Heavy Ion Collisions (2011, result): “Our discussion will closely follow the formalism developed in [369], which builds upon earlier analyses in Refs.”
Thermoelectric DC conductivities from black hole horizons (2014, background): “For example, for the D = 4 AdS-Schwarzschild black hole we get σ = Zs/(4πe2V1), for constant Z, recovering the result of [3].”