We calculate the total cross section for deep inelastic scattering (DIS) on a nucleus at high energy for a strongly coupled N = 4 super Yang-Mills theory using AdS/CFT correspondence. In analogy to the small coupling case we argue that at high energy the total DIS cross section is related to the expectation value of the Wilson loop formed by the quark-antiquark dipole. We model the nucleus by a metric of a shock wave in AdS 5 . We then calculate the expectation value of the Wilson loop by finding the extrema of the Nambu-Goto action for an open string attached to the quark and antiquark lines of the loop in the background of an AdS 5 shock wave. We find three extrema of the Nambu-Goto action: the string coordinates at the extrema are complex-valued and are given by three different branches of the solution of a cubic equation. The physically meaningful solutions for the total DIS cross section are given either by the only branch with a purely imaginary string coordinate in the bulk or by a superposition of the two other branches. For both solutions we obtain the forward scattering amplitude N for the quark dipole-nucleus scattering. We study the onset of unitarity with increasing center-of-mass energy and transverse size of the dipole: we observe that for both solutions the saturation scale, while energy-dependent at lower energies, at very high energy becomes independent of energy/Bjorken-x. The saturation scale depends very strongly on the atomic number of the nucleus as Q s ∼ A 1/3 . While the infinite mass of the "quarks" justifies the recoilless approximation for their interaction with the target, the question arises of applicability of this model to the description of real DIS processes with light quarks, which indeed recoil during the interaction. For instance, while at small coupling in the leading logarithmic α s ln 1/x Bj approximation the recoilless approximation is justified [19,21,17,18], its validity becomes less clear at the subleading logarithmic order (order α 2 s ln 1/x Bj ) [39]. We note that the recoil of the quarks at high energy only affects the impact factors (see e.g. [84]), and not the part of the interaction described by the small-x Bj evolution. Thus the calculation below, when applied to light quarks, should be understood as calculation of the evolution without the impact factors. While the impact factors are likely to be numerically important, we will proceed under the assumption that they will not affect the qualitative features of the obtained scattering amplitude.

We construct a model of high energy heavy ion collisions as two ultrarelativistic shock waves colliding in AdS 5 . We point out that shock waves corresponding to physical energymomentum tensors of the nuclei completely stop almost immediately after the collision in AdS 5 , which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Since in real-life heavy ion collisions the large Bjorken x part of nuclear wave functions continues to move along the light cone trajectories of the incoming nuclei leaving the small-x partons behind, we conclude that a pure large coupling approach is not likely to adequately model nuclear collisions. We show that to account for small-coupling effects one can model the colliding nuclei by two (unphysical) ultrarelativistic shock waves with zero net energy each (but with non-zero energy density). We use this model to study the energy density of the strongly-coupled matter created immediately after the collision. We argue that expansion of the energy density ǫ in the powers of proper time τ squared corresponds on the gravity side to a perturbative expansion of the metric in graviton exchanges. Using such expansion we reproduce our earlier result [1] that the energy density of produced matter at mid-rapidity starts out as a constant (of time) in heavy ion collisions at large coupling.

We study the matter produced in heavy ion collisions assuming that this matter is strongly interacting and employing AdS/CFT correspondence to investigate its dynamics. At late proper times τ we show that Bjorken hydrodynamics solution, obtained recently by Janik and Peschanski using gauge-gravity duality [1], can be singled out by simply requiring that the metric tensor is a real and single-valued function of the coordinates everywhere in the bulk, without imposing any constraints on the curvature invariant. At early proper times we use similar strategy to show that the energy density ǫ approaches a constant as τ → 0. We therefore demonstrate that the strong coupling dynamics incorporates the isotropization transition in heavy ion collisions. By matching our earlytime regime with the late-time one of Janik and Peschanski we estimate the isotropization time at RHIC to be approximately τ iso ≈ 0.3 fm/c, in good agreement with results of hydrodynamic simulations. *

We consider high energy collisions of two shock waves in AdS 5 as a model of ultrarelativistic nucleus-nucleus collisions in the boundary theory. We first calculate the graviton field produced in the collisions in the NLO and NNLO approximations, corresponding to three-and four-graviton exchanges with the shock waves. We then consider the asymmetric limit where the energy density in one shock wave is much higher than in the other one. In the boundary theory this setup corresponds to proton-nucleus collisions, with the nucleus being the denser of the two shock waves and the proton being the less dense one. Employing the eikonal approximation we find the exact high energy analytic solution for the metric in AdS 5 for the asymmetric collision of two delta-function shock waves. The solution resums all-order graviton exchanges with the "nucleus" shock wave and a single-graviton exchange with the "proton" shock wave. Using the holographic renormalization prescription we read off the energy-momentum tensor of the matter produced in proton-nucleus collisions. We show in explicit detail that in the boundary theory the proton is completely stopped by strong-coupling interactions with the nucleus, in agreement with our earlier results [1]. We also apply the eikonal technique to the asymmetric collision of two unphysical delta-prime shock waves, which we introduced in [1] as a means of modeling nuclear collisions with weak coupling initial dynamics. We obtain a surprising result that, for delta-prime shock waves, the multiple bulk graviton exchange series giving the leading energy-dependent contribution to the energy-momentum tensor terminates at the order of two graviton exchanges with the nucleus.

We develop a general framework for computing the holographic 2-point functions and the corresponding conductivities in asymptotically locally AdS backgrounds with an electric charge density, a constant magentic field, and possibly non-trivial scalar profiles, for a broad class of Einstein-Maxwell-Axion-Dilaton theories, including certain Chern-Simons terms. Holographic renormalization is carried out for any theory in this class and the computation of the renormalized AC conductivities at zero spatial momentum is reduced to solving a single decoupled first order Riccati equation. Moreover, we develop a first order fake supergravity formulalism for dyonic renormalization group flows in four dimensions, allowing us to construct analytically infinite families of such backgrounds by specifying a superpotential at will. These RG flows interpolate between AdS 4 in the UV and a hyperscaling violating Lifshitz geometry in the IR with exponents 1 < z < 3 and θ = z + 1. For 1 < z < 2 the spectrum of fluctuations is gapped and discrete. Our hope and intention is that this analysis can serve as a manual for computing the holographic 1-and 2-point functions and the corresponding transport coefficients in any dyonic background, both in the context of AdS/CMT and AdS/QCD. 1 We write µνρσ = e µ a e ν b e ρ c e σ d abcd with ntxy = 1, wheren is the Lorentz frame index corresponding to the direction orthogonal to the boundary of ∂M in M.

We revisit the calculation of a heavy quark potential in N = 4 supersymmetric Yang-Mills theory at finite temperature using the AdS/CFT correspondence. As is widely known, the potential calculated in the pioneering works of Rey et al. [1] and Brandhuber et al. [2] is zero for separation distances r between the quark and the anti-quark above a certain critical separation, at which the potential has a kink. We point out that by analytically continuing the string configurations into the complex plane, and using a slightly different renormalization subtraction, one obtains a smooth non-zero (negative definite) potential without a kink. The obtained potential also has a non-zero imaginary (absorptive) part for separations r > rc = 0.870/πT . Most importantly at large separations r the real part of the potential does not exhibit the exponential Debye falloff expected from perturbation theory and instead falls off as a power law, proportional to 1/r 4 for r > r0 = 2.702/πT .Heavy quark potential is a very important quantity in gauge theories at finite temperature. It also has a great phenomenological relevance in connection with experimental programs in heavy ion collisions at the Relativistic Heavy Ion Collider and at the upcoming Large Hadron Collider. The melting of heavy mesons in a medium is considered to be one of the main experimental signatures for Quark-Gluon Plasma formation, the ultimate goal of such experiments. Current analyses of available experimental data indicate that the matter formed in such collisions is strongly coupled. Thus, the study of heavy quark potential requires strong-coupling techniques, such as the Anti-de Sitter space/conformal field theory (AdS/CFT) correspondence [3,4,5,6]. The main goal of this work is to improve the current description of heavy quark potential at finite temperature in the AdS/CFT framework.Until recently heavy quark potential has been calculated either analytically at small coupling using the perturbation theory, or numerically using lattice simulations. With the advent of AdS/CFT correspondence [3,4,5,6], it became possible to analytically calculate the heavy quark potential at strong coupling, albeit only for the N = 4 supersymmetric Yang-Mills (SYM) theory.The first calculation of a heavy quark potential in vacuum for N = 4 SYM theory was carried out by Maldacena in [7]. Soon after [7] calculations of the heavy quark potential for N = 4 SYM theory at finite temperature appeared in [1,2]. In [7] the heavy quark potential is obtained from the expectation value of a static temporal Wilson loop and in [1, 2] from the correlator of two Polyakov loops. They are calculated by extremizing the world-sheet of an open string attached to the quark and anti-quark located at the edge of the AdS 5 space in the background of the empty AdS 5 space in [7] and in the background of the AdS 5 black hole metric in [1,2].The zero-temperature heavy quark potential obtained in [7] is of Coulomb type due to conformal invariance of N = 4 SYM theory:with λ the 't Hooft coupling and c 0 = Γ ...

We study a simple example of holographic thermalization in a confining field theory: the homogeneous injection of energy in the hard wall model. Working in an amplitude expansion, we find black brane formation for sufficiently fast energy injection and a scattering wave solution for sufficiently slow injection. We comment on our expectations for more sophisticated holographic QCD models.

The formation of trapped surfaces in the head-on collision of shock waves in conformal and non-conformal backgrounds is investigated. The backgrounds include all interesting confining and non-confining backgrounds that may be relevant for QCD. Several transverse profiles of the shocks are investigated including distributions that fall-off as powers or exponentials. Different ways of cutting-off the UV contributions (that are expected to be perturbative in QCD) are explored. Under some plausible simplifying assumptions our estimates are converted into predictions for multiplicities for heavy-ion collisions at RHIC and LHC.