Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma

TL;DR

This paper investigates the shear viscosity and conductivity of an anisotropic strongly coupled plasma using holography, revealing violations of the viscosity bound in certain directions without higher-derivative gravity theories.

Contribution

It demonstrates that in an anisotropic holographic plasma, the shear viscosity bound is violated in the longitudinal direction, providing a novel example with a fully known gauge-gravity duality.

Findings

Transverse shear viscosity saturates the holographic bound.

Longitudinal shear viscosity is smaller than the bound.

The model is based on a known gauge-gravity duality without higher derivatives.

Abstract

We study the conductivity and shear viscosity tensors of a strongly coupled N=4 super-Yang-Mills plasma which is kept anisotropic by a theta parameter that depends linearly on one of the spatial dimensions. Its holographic dual is given by an anisotropic axion-dilaton-gravity background and has recently been proposed by Mateos and Trancanelli as a model for the pre-equilibrium stage of quark-gluon plasma in heavy-ion collisions. By applying the membrane paradigm which we also check by numerical evaluation of Kubo formula and lowest lying quasinormal modes, we find that the shear viscosity purely transverse to the direction of anisotropy saturates the holographic viscosity bound, whereas longitudinal shear viscosities are smaller, providing the first such example not involving higher-derivative theories of gravity and, more importantly, with fully known gauge-gravity correspondence.