# Hyperscaling violation, quasinormal modes and shear diffusion

Mukherjee, Debangshu  (Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, 603103, India) ; Narayan, Krishnan (Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, 603103, India)

07 December 2017

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 / 4 π for the viscosity-to-entropy-density ratio for all z ≤ d i + 2 − θ .

Published in: JHEP 1712 (2017) 023