Hyperscaling violation and the shear diffusion constant

Abstract

We consider holographic theories in bulk $(d+1)$-dimensions with Lifshitz and hyperscaling violating exponents $z,\theta$ at finite temperature. By studying shear gravitational modes in the near-horizon region given certain self-consistent approximations, we obtain the corresponding shear diffusion constant on an appropriately defined stretched horizon, adapting the analysis of Kovtun, Son and Starinets. For generic exponents with $d-z-\theta >-1$, we find that the diffusion constant has power law scaling with the temperature, motivating us to guess a universal relation for the viscosity bound. When the exponents satisfy $d-z-\theta =-1$, we find logarithmic behaviour. This relation is equivalent to $z=2+d_{eff}$ where $d_{eff}=d_i-\theta$ is the effective boundary spatial dimension (and $d_i=d-1$ the actual spatial dimension). It is satisfied by the exponents in hyperscaling violating theories arising from null reductions of highly boosted black branes, and we comment on the corresponding analysis in that context.

Latex, 17pgs, v3: clarifications added on z<2+d_{eff} and standard quantization, to be published

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Cited by in corpus (12)

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• Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
• Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity
• Greybody Factors of Holographic Superconductors with $z=2$ Lifshitz Scaling
• Hyperscaling violation, quasinormal modes and shear diffusion
• Holographic Dissipative Properties of Non-relativistic Black Branes with Hyperscaling Violation
• Holography of electrically and magnetically charged black branes
• Notes on hyperscaling violating Lifshitz and shear diffusion
• Quark anti-quark entropic force and diffusion constant in a Yang-Mills like theory
• Flow of shear response functions in hyperscaling violating Lifshitz theories