Magnetically-Charged Black Branes and Viscosity/Entropy Ratios

TL;DR

This paper investigates magnetically charged black branes in AdS space, analyzing their viscosity/entropy ratios and showing violations of the KSS bound, including extensions with scalar fields leading to Lifshitz geometries.

Contribution

It provides new solutions with magnetic charges affecting viscosity ratios and explores violations of the KSS bound in these contexts, including Lifshitz and hyperscaling-violating backgrounds.

Findings

KSS bound is generally violated in these magnetically charged solutions.

Derived explicit expressions for shear viscosity to entropy density ratio.

Extended analysis to Lifshitz geometries with hyperscaling violation.

Abstract

We consider asymptotically-AdS $n$-dimensional black brane solutions in a theory of gravity coupled to a set of $N$ $p$-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. We then study the linearised equation for transverse traceless metric perturbations in these backgrounds, and by employing the Kubo formula we obtain expressions for $\eta/S$, the ratio of shear viscosity to entropy density. We find that the KSS bound on the ratio $\eta/S$ is generally violated in these solutions. We also extend the discussion by including also a dilatonic scalar field in the theory, leading to solutions that are asymptotically Lifshitz with hyperscaling violation.