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 ∼ Tκ. We find the exponent κ can be greater than two such that the new bound for viscosity raised in [7] 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.