Notes on hyperscaling violating Lifshitz and shear diffusion
arXiv:1612.05950 · doi:10.1103/PhysRevD.96.026003
Abstract
We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in arXiv:1604.05092 [hep-th]. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicated. We find a similar near-horizon analysis can be obtained in terms of new field variables involving a linear combination of the metric and the gauge field perturbation resulting in a corresponding diffusion equation. Thereby as before, for theories with Lifshitz and hyperscaling violating exponents satisfying in four bulk dimensions, our analysis here results in a similar expression for the shear diffusion constant with power-law scaling with temperature suggesting universal behaviour in relation to the viscosity bound. For , we find logarithmic behaviour.
Latex, 38pgs, v2: references added
References in corpus (27)
- Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
- Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
- Nonlinear Fluid Dynamics from Gravity
- Effective Holographic Theories for low-temperature condensed matter systems
- Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
- Non-relativistic holography
- Universal Charge Diffusion and the Butterfly Effect
- Precision holography for non-conformal branes
- Universal hydrodynamics of non-conformal branes
- Lifshitz Solutions of D=10 and D=11 supergravity
- Holographic RG flow of the shear viscosity to entropy density ratio in strongly coupled anisotropic plasma
- Domain Wall Holography for Finite Temperature Scaling Solutions
- Lifshitz holography: The whole shebang
- A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography
- Conductivity and Diffusion Constant in Lifshitz Backgrounds
- Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance
- Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
- Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum
- Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity
- Hyperscaling-Violating Lifshitz hydrodynamics from black-holes: Part II
- AdS plane waves, entanglement and mutual information
- Hyperscaling violation and the shear diffusion constant
- Power Law of Shear Viscosity in Einstein-Maxwell-Dilaton-Axion model
- Hydrodynamics from scalar black branes
- On a lightlike limit of entanglement
- Hydrodynamics in black brane with hyperscaling violation metric background
- Holographic charge diffusion in non relativistic branes