2016/01/31 by Sean A. Hartnoll, David M. Ramirez, Jorge E. Santos · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep03(2016)170
1 + 22 pages + appendices. 7 figures. v2 references added
arxiv created 2016/02/05 · arxiv updated 2016/04/20
The ratio of shear viscosity to entropy density, η/s, is computed in various holographic geometries that break translation invariance (but are isotropic). The shear viscosity does not have a hydrodynamic interpretation in such backgrounds, but does quantify the rate of entropy production due to a strain. Fluctuations of the metric components δgxy are massive about these backgrounds, leading to η/s < 1/(4π) at all finite temperatures (even in Einstein gravity). As the temperature is taken to zero, different behaviors are possible. If translation symmetry breaking is irrelevant in the far IR, then η/s tends to a constant at T=0. This constant can be parametrically small. If the translation symmetry is broken in the far IR (which nonetheless develops emergent scale invariance), then η/s ∼ T2 ν as T → 0, with ν≤ 1 in all cases we have considered. While these results violate simple bounds on η/s, we note that they are consistent with a possible bound on the rate of entropy production due to strain.