Hyperscaling violation, quasinormal modes and shear diffusion

We study quasinormal modes of shear gravitational perturbations for hyper scaling 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 di 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 <= 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 <= d(i) + 2 - theta.