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 θ. 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 − θ where d i is the boundary spatial dimension, the shear diffusion constant exhibits power-law scaling with temperature, while for z = d i + 2 − θ, it exhibits logarithmic scaling. We then calculate certain 2-point functions of the dual energy-momentum tensor holographically for z ≤ d i + 2 − θ, identifying the diffusive poles with the quasinormal modes above. This reveals universal behaviour η/s = 1/4π for the viscosity-to-entropy-density ratio for all z ≤ d i + 2 − θ