The Hydrodynamics of M-Theory

By Christopher P. Herzog. 2002

187 citations recorded by the source corpus.

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets hep-th/0205051. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/acef9e72c5290cef20ec4d83b88326bd109f9547

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Citations in the corpus

Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang–Mills theory (2004, background): “The same feature holds for theories dual to M-branes [24, 25].”
Dissecting holographic conductivities (2015, methodology): “This procedure was used in [28–30] to determine the two-point Green’s functions of translationally invariant systems at small frequencies.”
Holography and hydrodynamics: Diffusion on stretched horizons (2003, methodology): “The AdS/CFT calculation [12] shows that the R-current relaxes diffusively, with the diffusion constant equal to 3/(4πT ), and that the shear mode damping constant is 1/4πT .”
The dS/dS Correspondence (2004, methodology): “[29,30,31, 32 ] using purely outgoing boundary conditions on the horizon to reflect the dissi-”
Lectures on holographic methods for condensed matter physics (2009, background): “[96, 97], arise because the coefficient of the 1/ω term in (156) is effectively taken to zero.”
Quantum magnetism and criticality (2007, background): “(22) and (23), including the exact values [71, 72] of the numbers K, Θ1, Θ2.”
From AdS/CFT correspondence to hydrodynamics. II. Sound waves (2002, background): “[12] to M2 and M5 branes of M-theory, where hydrodynamic behavior is also observed, although the worldvolume theories in these cases are not well understood.”
On universality of stress-energy tensor correlation functions in supergravity (2004, background): “The relevant set of supergravity backgrounds includes all geometries which can be interpreted via gauge theory/string theory correspondence as being holographically dual to finite temperature gauge theories in Minkowski space-times.”
Ohm's law at strong coupling: S duality and the cyclotron resonance (2007, background): “[12] calculated the viscosity and R-charge diffusion constants (1)These CFTs typically have a parameter N which counts the number of degrees of freedom and needs to be kept parametrically large.”
From AdS/CFT correspondence to hydrodynamics. II. Sound waves (2002, background): “drodynamic regime of the correlators in N = 4 SYM theory at ﬁnite temperature, which is another testimony to the validity of the correspondence. The calculations of ref. [6] has been extended in ref. [12] to M2 and M5 branes of M-theory, where hydrodynamic behavior is also observed, although the wor”
Impure AdS/CFT correspondence (2008, unknown): “16 93 v2 [”
Wilsonian approach to fluid/gravity duality (2010, background): “A quarter century later, ηs = 1 4π reappeared in a beautiful paper by Policastro, Starinets and Son (PSS)[11], see also [12-28] and the review [29].”
Mimicking the QCD equation of state with a dual black hole (2008, background): “This immediately points to a weakness of our approach: the shear viscosity will always satisfy η/s = 1/4π, regardless of temperature [41, 42, 43, 44].”