Hyperscaling violation, quasinormal modes and shear diffusion

TL;DR

This paper investigates shear quasinormal modes in hyperscaling violating Lifshitz theories, confirming the shear diffusion constant's scaling behavior and the universal viscosity-to-entropy ratio through holographic methods.

Contribution

It provides a detailed analysis of quasinormal modes and shear diffusion in hyperscaling violating Lifshitz backgrounds, extending understanding of transport properties in these theories.

Findings

Shear diffusion constant matches previous results.

Diffusive poles identified in 2-point functions.

Universal ratio η/s=1/4π confirmed for certain parameters.

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 $z\leq d_i+2-\theta$, 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 $z\leq d_i+2-\theta$.