AnisotropicN=4Super-Yang-Mills Plasma and Its Instabilities

Abstract

We present a IIB supergravity solution dual to a spatially anisotropic finite-temperature N = 4 super Yang-Mills plasma. The solution is static and completely regular. The full geometry can be viewed as a renormalization group flow from an ultraviolet AdS geometry to an infrared Lifshitz-like geometry. 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.1. Introduction. The realization that the quark-gluon plasma (QGP) produced in heavy ion collisions (HIC) is strongly coupled [1] has provided motivation for understanding the dynamics of strongly coupled non-Abelian plasmas through the gauge/string duality [2] (see [3] for a review of applications to the QGP). The simplest example of the duality is the equivalence between fourdimensional N = 4 SU (N c ) super Yang-Mills (SYM) theory and IIB string theory on AdS 5 × S 5 . Here we extend this example to the case in which the SYM plasma is spatially anisotropic. For accessibility by a broad audience, details will appear elsewhere [4]. Previous holographic studies of anisotropic plasmas include [5,6]. One important difference with the gravity solution of [6] is that the latter possesses a naked singularity, whereas our solution is completely regular.

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).…”

Shock waves in Lifshitz-like spacetimes

“…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].…”

“…In this paper, we consider Lifshitz-like backgrounds in the context of their applications to the anisotropic quark-gluon plasma created in heavy-ion collisions [35]- [46]. 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].…”

“…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.…”

Flowing from AdS5 to AdS3 with T 1,1

“…In particular, as we will see, the T 2 essentially just comes along for the ride. Now we consider the gauge for the two-form B given in the N N patch by 33) which is clearly well defined in U N N . We see that it is also well defined in U SN , after using (2.32).…”