We study the conductivity and shear viscosity tensors of a strongly coupled N = 4 super-YangMills plasma which is kept anisotropic by a θ parameter that depends linearly on one of the spatial dimensions. Its holographic dual is given by an anisotropic axion-dilaton-gravity background and has recently been proposed by Mateos and Trancanelli as a model for the pre-equilibrium stage of quark-gluon plasma in heavy-ion collisions. By applying the membrane paradigm which we also check by numerical evaluation of Kubo formula and lowest lying quasinormal modes, we find that the shear viscosity purely transverse to the direction of anisotropy saturates the holographic viscosity bound, whereas longitudinal shear viscosities are smaller, providing the first such example not involving higher-derivative theories of gravity and, more importantly, with fully known gaugegravity correspondence.PACS numbers: 11.25. Tq, 11.10Wx, 12.38.Mh Introduction. Hydrodynamic simulations of heavyion collisions suggest [1] that the produced quark-gluon plasma is behaving like an almost perfect fluid with a ratio of shear viscosity over entropy density not far from the famous result /4π associated with the membrane paradigm of black holes [2] and which holographic gaugegravity duality maps to the corresponding quantity of maximally supersymmetric Yang-Mills theory in the limit of infinite color number and infinite 't Hooft coupling [3,4]. This value has been conjectured to form the lower bound for any realistic matter [5]. It was found to be saturated universally [6,7] in dual theories involving an isotropic horizon described by Einstein gravity. Values above this bound are obtained when corrections due to finite coupling strength are included [8], but it has been shown that values violating the bound can arise in higherderivate gravities [9], although so far no complete gaugegravity correspondence has been established for finite violations.

We use the AdS/CFT conjecture to investigate the thermalization of large-N(c) N = 4 super Yang-Mills plasma in the limit of large but finite 't Hooft coupling. On the gravity side, we supplement the type IIB supergravity action by the full set of O(α('3)) operators, which enables us to derive O(λ(-3/2)) corrections to the emission spectrum of prompt photons in one model of holographic thermalization. Decreasing the coupling strength from the λ = ∞ limit, we observe a qualitative change in the way the photon spectral density approaches its thermal limit as a function of the photon energy. We interpret this behavior as a sign of the thermalization pattern of the plasma shifting from top-down towards bottom-up.

The time evolution of collective modes in an expanding ultarelativistic and (effectively) Abelian plasma is studied in the hard-loop approximation semi-analytically by means of integro-differential equations. A previous treatment is generalized to arbitrary orientation of wave vectors with respect to the direction of anisotropy and thus to a fully 3+1 dimensional situation. Moreover, initial fluctuations are allowed in both gauge fields and currents, which is necessary in the case of (stable) longitudinal modes. For unstable (Weibel) modes, this generalization of initial conditions reduces drastically the lower bound on the delay in the onset of growth that was found previously by considering only collective gauge fields as seeds. This makes it appear much more likely that non-Abelian plasma instabilities seeded by small initial rapidity fluctuations could play an important role in the early stage of heavyion collisions at LHC energies.

We investigate the behavior of the retarded Green's function of a U(1) gauge field in holographic N = 4 Super Yang-Mills plasma, taking the leading strong coupling corrections into account. First, we use the thermal limit of this quantity to determine the flow of the photon quasinormal mode spectrum away from the infinite 't Hooft coupling limit, and after this specialize to a specific model of holographic thermalization, in which we evaluate the corresponding spectral density. In the latter case, our primary interest lies in the pattern, with which the spectral density approaches its equilibrium form, and how this process depends on the value of the coupling as well as the photon virtuality. All of the results obtained point consistently towards the weakening of the usual top/down pattern of holographic thermalization, once the coupling is decreased from the λ = ∞ limit.

Quark-gluon plasma during its initial phase after its production in heavy-ion collisions is expected to have substantial pressure anisotropies. In order to model this situation by a strongly coupled N = 4 super-Yang-Mills plasma with fixed anisotropy by means of AdS/CFT duality, two models have been discussed in the literature. Janik and Witaszczyk have considered a geometry involving a comparatively benign naked singularity, while more recently Mateos and Trancanelli have used a regular geometry involving a nontrivial axion field dual to a parity-odd deformation of the gauge theory by a spatially varying θ parameter. We study the (rather different) implications of these two models on the heavy-quark potential as well as jet quenching and compare their respective predictions with those of weakly coupled anisotropic plasmas.