Anisotropic plasma with a chemical potential and scheme-independent instabilities

Abstract

Generically, the black brane solution with planar horizons is thermodynamically stable. We find a counter-example to this statement by demonstrating that an anisotropic black brane is unstable. We present a charged black brane solution dual to a spatially anisotropic finite temperature $\mathcal{N}=4$ super Yang-Mills plasma at finite $U(1)$ chemical potential. This static and regular solution is obtained both numerically and analytically. We uncover rich thermodynamic phase structures for this system by considering the cases when the anisotropy constant "a" takes real and imaginary values, respectively. In the case $a^2>0$, the phase structure of this anisotropic black brane is similar to that of Schwarzschild-AdS black hole with $S^3$ horizon topology, yielding a thermodynamical instability at smaller horizon radii. For the condition $a^2\le 0$, the thermodynamics is dominated by the black brane phase for all temperatures.

14pages,14figures, minor changes, PLB in press

References in corpus (4)

• Building an AdS/CFT superconductor
• Lectures on Holographic Superfluidity and Superconductivity
• Jet Quenching Parameter in Medium with Chemical Potential from AdS/CFT
• Highly anisotropic hydrodynamics -- discussion of the model assumptions and forms of the initial conditions

Cited by in corpus (11)

• Anisotropic plasma at finite $U(1)$ chemical potential
• Thermoelectric DC conductivities with momentum dissipation from higher derivative gravity
• Holographic renormalization and anisotropic black branes in higher curvature gravity
• Anisotropic Fermi surface from holography
• Viscosity bound for anisotropic superfluids in higher derivative gravity
• Thermodynamics of anisotropic branes
• Drag force in strongly coupled, anisotropic plasma at finite chemical potential
• Holographic study on the jet quenching parameter in anisotropic systems
• Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale
• Stability analysis of (a class of) anisotropic spacetimes
• Effects of hyperscaling violation and dynamical exponents on drag force