Holographic Turbulence in a Large Number of Dimensions

Abstract

We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large number of dimensions satisfy the aforementioned restrictions and their dynamics are captured by hydrodynamics with a naturally truncated derivative expansion. Using analytic and numerical techniques we analyze two and three-dimensional turbulent flow of such fluids in various regimes and its relation to geometric data.

36 pages, 22 figures

References in corpus (9)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonlinear Fluid Dynamics from Gravity
• Universal hydrodynamics of non-conformal branes
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• The large D black hole Membrane Paradigm at first subleading order
• Unstable `black branes' from scaled membranes at large $D$
• Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence
• Non-linear perturbation of black branes at large $D$

Cited by in corpus (21)

• Holographic Collisions across a Phase Transition
• The Large D Limit of Einstein's Equations
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Rotating black holes and black bars at large D
• An Action for and Hydrodynamics from the improved Large D membrane
• Black holes in presence of cosmological constant: Second order in 1/D
• Holographic Bjorken Flow at Large-D
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• Large D holography with metric deformations
• Stationary Solutions from the Large D Membrane Paradigm
• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Holographic Observables at Large $d$
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• A leading-order comparison between fluid-gravity and membrane-gravity dualities
• Stochastic gravity and turbulence
• Black hole interactions at large $D$: brane blobology
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Lattice Black Branes at Large $D$
• Stress Tensor for Large-$D$ membrane at subleading orders
• An analytic approach for holographic entanglement entropy at (quantum) criticality
• Critical transition to a non-chaotic regime in isotropic turbulence