The shear viscosity of the non-commutative plasma

TL;DR

Investigates the shear viscosity of a strongly coupled non-commutative N=4 SYM plasma using its gravity dual. It emphasizes anisotropy from the non-commutative plane and defines the holographic stress tensor via the open-string metric. Through scalar and vector fluctuation analyses, it demonstrates η/s = 1/4π in all relevant shear channels, consistent with the universal bound, and shows the finite-temperature stress tensor matches the commutative theory. The work also discusses holographic renormalization in this non-commutative setting and the role of open-string data in reconciling the boundary theory with bulk gravity.

Abstract

We compute the shear viscosity of the non-commutative N=4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/s = 1/4πfor two different shear channels. In order to derive this result, we show that the boundary energy momentum tensor must couple to the open string metric. As a byproduct we compute the renormalised holographic energy momentum tensor and show that it coincides with one in the commutative theory.