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

We study the conductivity and shear viscosity tensors of a strongly coupled $\mathcal{N}=4$ 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 preequilibrium 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.

Figure 1

The dc conductivities along and transverse to the direction of anisotropy as a function of the anisotropy parameter $a/T$.

Figure 2

Transverse and longitudinal shear viscosities over $s/4\pi$ as a function of the anisotropy parameter $a/T$.