Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance

In this paper we investigate the ratio of shear viscosity to entropy density, $η/s$, 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, $η/s\sim T^κ$. We find the exponent $κ$ 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 $κ$ with the behavior of entanglement entropy and conjecture a relation between them.

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