Thermodynamics and instabilities of a strongly coupled anisotropic plasma

Abstract

We extend our analysis of a IIB supergravity solution dual to a spatially anisotropic finitetemperature 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 θ-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. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

The shear viscosity in anisotropic phases

“…The behaviour of the viscosity discussed above refers to isotropic and homogeneous phases, which on the gravity side at finite temperature are described by the Schwarzschild black brane geometry. More recently, gravitational backgrounds which correspond to anisotropic phases in field theory have also been studied in [8,[14][15][16][17][18][19][20][21] and the behaviour of the viscosity in some of these anisotropic phases has also been analysed, see [22,23] and [24][25][26][27][28][29]. The viscosity in the anisotropic case is a tensor, which in the most general case, with no rotational invariance, has 21 independent components (when the field theory lives in 3 + 1 dimensions).…”

“…(5.17). The conductivity is given by 20) where Z and Π are the asymptotic values of the perturbation and conjugate momentum defined in eq. (5.19) in the region u → ∞.…”

Shock waves in Lifshitz-like spacetimes

“…In [35,36] the finite-temperature generalization of the type IIB supergravity solution of [34] was studied as a gravity dual to an anisotropic deformation of a four-dimensional N = 4 super Yang-Mills theory. It was noted in [36] that at zero temperature the metric has a naked curvature singularity deep in the IR.…”

“…It was noted in [36] that at zero temperature the metric has a naked curvature singularity deep in the IR. The existence of solutions which interpolate between the anisotropic solutions in the IR and the AdS 5 × X 5 solutions in the UV was shown in [34,36]. These interpolating solutions can be considered as the dual of the RG flow between the two systems [35,36].…”

“…A holographic model with a Lifshitz-like spacetime in the IR and AdS boundary conditions is supposed to be related with an anisotropic SYM quark-gluon plasma [36]. Several physical quantities have been explored in this frameworks.…”