Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance

TL;DR

This paper explores how hyperscaling violation and lattice structures in holographic models affect the shear viscosity to entropy density ratio, revealing violations of previously proposed bounds and suggesting a link to entanglement entropy.

Contribution

It demonstrates that hyperscaling violation can lead to shear viscosity exponents exceeding prior bounds and constructs specific holographic solutions to support this.

Findings

The shear viscosity to entropy density ratio can scale as T^κ with κ > 2.

The new viscosity bound proposed in prior work can be violated.

A potential relation between viscosity scaling and entanglement entropy is conjectured.

Abstract

In this paper we investigate the ratio of shear viscosity to entropy density, $\eta/s$, in hyperscaling violating geometry with lattice structure. We show that the scaling relation with hyperscaling violation gives a strong constraint to the mass of graviton and usually leads to a power law of temperature, $\eta/s\sim T^\kappa$. We find the exponent $\kappa$ can be greater than two such that the new bound for viscosity raised in arXiv:1601.02757 is violated. Our above observation is testified by constructing specific solutions with UV completion in various holographic models. Finally, we compare the boundedness of $\kappa$ with the behavior of entanglement entropy and conjecture a relation between them.