The anisotropic N=4 super Yang-Mills plasma and its instabilities

TL;DR

A type-IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super-Yang-Mills plasma is presented, commenting on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

Abstract

We present a IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent theta-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics of the system. We construct the phase diagram, which exhibits homogeneous and inhomogeneous (i.e. mixed) phases, and comment on similarities with QCD at finite baryon density. At low densities the homogeneous phase displays several instabilities reminiscent of instabilities of weakly coupled plasmas.

Figures (1)

• Figure 1: (Left) Entropy density as a function of $a/T$. (Center) Energy and pressures as functions of $T/a$ for fixed $a\simeq 2.86$ and $\log \mu=1/2$. (Right) Qualitative phase diagram.