Magnetically-charged black branes and viscosity/entropy ratios

We consider asymptotically-AdS n-dimensional black brane solutions in a theory of gravity coupled to a set of Np-form field strengths, in which the field strengths carry magnetic charges. For appropriately chosen charges, the metrics are isotropic in the (n−2) transverse directions. However, in general the field strength configurations break the full Euclidean symmetry of the (n−2)-dimensional transverse space, and the shear viscosity tensor in the dual theory is no longer isotropic. We study the linearised equations for transverse traceless metric perturbations in these backgrounds, and by employing the Kubo formula we obtain expressions for the ratios η/S of the shear viscosity components divided by the entropy density. We find that the KSS bound on the ratios η/S is generally violated in these solutions. We also extend the discussion by including a dilatonic scalar field in the theory, leading to solutions that are asymptotically Lifshitz with hyperscaling violation.