Hyperscaling violation, quasinormal modes and shear diffusion

Abstract

We study quasinormal modes of shear gravitational perturbations for hyperscaling violating Lifshitz theories, with Lifshitz and hyperscaling violating exponents $z$ and $\theta$. The lowest quasinormal mode frequency yields a shear diffusion constant which is in agreement with that obtained in previous work by other methods. In particular for theories with $z<d_i+2-\theta$ where $d_i$ is the boundary spatial dimension, the shear diffusion constant exhibits power-law scaling with temperature, while for $z=d_i+2-\theta$, it exhibits logarithmic scaling. We then calculate certain 2-point functions of the dual energy-momentum tensor holographically for $z\le d_i+2-\theta$, identifying the diffusive poles with the quasinormal modes above. This reveals universal behaviour $\eta /s=1/4\pi$ for the viscosity-to-entropy-density ratio for all $z\le d_i+2-\theta$.

v2: Latex, 21pgs, more details of analysis, review of shear diffusion from membrane paradigm, references added, matches version to be published

References in corpus (26)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Quasinormal modes of black holes and black branes
• AdS/CFT Correspondence and Symmetry Breaking
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Nonlinear Fluid Dynamics from Gravity
• From AdS/CFT correspondence to hydrodynamics
• Holography and hydrodynamics: diffusion on stretched horizons
• Aspects of holography for theories with hyperscaling violation
• Universal Charge Diffusion and the Butterfly Effect
• Holographic Fermi Surfaces and Entanglement Entropy
• Lifshitz/Schrödinger D-p-branes and dynamical exponents
• Quasinormal spectrum and the black hole membrane paradigm
• Conductivity and Diffusion Constant in Lifshitz Backgrounds
• Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity
• AdS plane waves and entanglement entropy
• Generating Temperature Flow for eta/s with Higher Derivatives: From Lifshitz to AdS
• Hyperscaling-Violating Lifshitz hydrodynamics from black-holes: Part II
• Non-conformal brane plane waves and entanglement entropy
• Transport coefficients from hyperscaling violating black brane: shear viscosity and conductivity
• Hyperscaling violation and the shear diffusion constant
• Hydrodynamics from scalar black branes
• Hydrodynamics in black brane with hyperscaling violation metric background
• Holographic charge diffusion in non relativistic branes

Cited by in corpus (4)

• Hyperscaling violating black holes with spherical and hyperbolic horizons
• $Ad{S}_2$ dilaton gravity from reductions of some nonrelativistic theories
• Greybody Factors of Holographic Superconductors with $z=2$ Lifshitz Scaling
• Flow of shear response functions in hyperscaling violating Lifshitz theories