Holographic shear viscosity in hyperscaling violating theories without translational invariance
Yi Ling (Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China, Shanghai Key Laboratory of High Temperature Superconductors, Shanghai, 200444, China); Zhuoyu Xian (Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China); Zhenhua Zhou (Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China)
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 ∼ T κ . 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.