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

TL;DR

This paper constructs a supergravity dual to an anisotropic, finite-temperature N=4 super Yang-Mills plasma, revealing its phase structure, instabilities, and thermodynamics, with potential insights into QCD-like behavior at finite density.

Contribution

It introduces a novel supergravity solution modeling anisotropic plasma with a detailed phase diagram and instability analysis, extending holographic methods to anisotropic systems.

Findings

The solution is regular, static, with an anisotropic horizon.

The phase diagram includes homogeneous and inhomogeneous phases.

Homogeneous phase exhibits instabilities similar to weakly coupled plasmas.

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.