The gauge-string duality and heavy ion collisions

I review at a non-technical level the use of the gauge-string duality to study aspects of heavy ion collisions, with special emphasis on the trailing string calculation of heavy quark energy loss. I include some brief speculations on how variants of the trailing string construction could provide a toy model of black hole formation and evaporation. This essay is an invited contribution to "Forty Years of String Theory" and is aimed at philosophers and historians of science as well as physicists.Comment: 21 page

Spinning Dragging Strings

We use the AdS/CFT correspondence to compute the drag force experienced by a heavy quark moving through a maximally supersymmetric SU(N) super Yang-Mills plasma at nonzero temperature and R-charge chemical potential and at large 't Hooft coupling. We resolve a discrepancy in the literature between two earlier studies of such quarks. In addition, we consider small fluctuations of the spinning strings dual to these probe quarks and find no evidence of instabilities. We make some comments about suitable D7-brane boundary conditions for the dual strings.Comment: 25 pages, 4 figures; v2 refs added; v3 to appear in JHEP, clarifying comment

Stirring Strongly Coupled Plasma

We determine the energy it takes to move a test quark along a circle of radius L with angular frequency w through the strongly coupled plasma of N=4 supersymmetric Yang-Mills (SYM) theory. We find that for most values of L and w the energy deposited by stirring the plasma in this way is governed either by the drag force acting on a test quark moving through the plasma in a straight line with speed v=Lw or by the energy radiated by a quark in circular motion in the absence of any plasma, whichever is larger. There is a continuous crossover from the drag-dominated regime to the radiation-dominated regime. In the crossover regime we find evidence for significant destructive interference between energy loss due to drag and that due to radiation as if in vacuum. The rotating quark thus serves as a model system in which the relative strength of, and interplay between, two different mechanisms of parton energy loss is accessible via a controlled classical gravity calculation. We close by speculating on the implications of our results for a quark that is moving through the plasma in a straight line while decelerating, although in this case the classical calculation breaks down at the same value of the deceleration at which the radiation-dominated regime sets in.Comment: 27 pages LaTex, 5 figure

Hard thermal loops and the entropy of supersymmetric Yang-Mills theories

We apply the previously proposed scheme of approximately self-consistent hard-thermal-loop resummations in the entropy of high-temperature QCD to N=4 supersymmetric Yang-Mills (SYM) theories and compare with a (uniquely determined) R[4,4] Pad\'e approximant that interpolates accurately between the known perturbative result and the next-to-leading order strong-coupling result obtained from AdS/CFT correspondence. We find good agreement up to couplings where the entropy has dropped to about 85% of the Stefan-Boltzmann value. This is precisely the regime which in purely gluonic QCD corresponds to temperatures above 2.5 times the deconfinement temperature and for which this method of hard-thermal-loop resummation has given similar good agreement with lattice QCD results. This suggests that in this regime the entropy of both QCD and N=4 SYM is dominated by effectively weakly coupled hard-thermal-loop quasiparticle degrees of freedom. In N=4 SYM, strong-coupling contributions to the thermodynamic potential take over when the entropy drops below 85% of the Stefan-Boltzmann value.Comment: 14 pages, 2 figures, JHEP3. v2: revised and expanded, with unchanged HTL results but corrected NLO strong-coupling result from AdS/CFT (which is incorrectly reproduced in almost all previous papers comparing weak and strong coupling results of N=4 SYM) and novel (unique) Pade approximant interpolating between weak and strong coupling result

Debye screening in strongly coupled N=4 supersymmetric Yang-Mills plasma

Using the AdS/CFT correspondence, we examine the behavior of correlators of Polyakov loops and other operators in N=4 supersymmetric Yang-Mills theory at non-zero temperature. The implications for Debye screening in this strongly coupled non-Abelian plasma, and comparisons with available results for thermal QCD, are discussed.Comment: 21 pages, 5 figures, significantly expanded discussion of Polyakov loop correlator and static quark-antiquark potentia

Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac monopole with a fine-tuned inverse-square plus Newtonian potential, introduced by McIntosh, Cisneros, and by Zwanziger some time ago. The trajectories are (arcs of) ellipses, which, in the commutative limit, reduce to the circular hodographs of the Kepler problem. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and actually extends to the conformal algebra o(4,2).Comment: 10 pages, 3 figures. Published versio

Localization of Gravity on Brane Embedded in AdS5AdS_5 and dS5dS_5

We address the localization of gravity on the Friedmann-Robertson-Walker type brane embedded in either $AdS_{5}$ or $dS_{5}$ bulk space,and derive two definite limits between which the value of the bulk cosmological constant has to lie in order to localize the graviton on the brane.The lower limit implies that the brane should be either $dS_{4}$ or 4d Minkowski in the $AdS_{5}$ bulk.The positive upper limit indicates that the gravity can be trapped also on curved brane in the $dS_{5}$ bulk space.Some implications to recent cosmological scenarios are also discussed.Comment: 18 pages, 3 figures, Latex fil

Five-Brane Configurations without a Strong Coupling Regime

Five-brane distributions with no strong coupling problems and high symmetry are studied. The simplest configuration corresponds to a spherical shell of branes with S^3 geometry and symmetry. The equations of motions with delta-function sources are carefully solved in such backgrounds. Various other brane distributions with sixteen unbroken supercharges are described. They are associated to exact world-sheet superconformal field theories with domain-walls in space-time. We study the equations of gravitational fluctuations, find normalizable modes of bulk 6-d gravitons and confirm the existence of a mass gap. We also study the moduli of the configurations and derive their (normalizable) wave-functions. We use our results to calculate in a controllable fashion using holography, the two-point function of the stress tensor of little string theory in these vacua.Comment: LateX, 32 pages, 4 figures; (v2) A reference adde

The dynamics of quark-gluon plasma and AdS/CFT

In these pedagogical lectures, we present the techniques of the AdS/CFT correspondence which can be applied to the study of real time dynamics of a strongly coupled plasma system. These methods are based on solving gravitational Einstein's equations on the string/gravity side of the AdS/CFT correspondence. We illustrate these techniques with applications to the boost-invariant expansion of a plasma system. We emphasize the common underlying AdS/CFT description both in the large proper time regime where hydrodynamic dynamics dominates, and in the small proper time regime where the dynamics is far from equilibrium. These AdS/CFT methods provide a fascinating arena interrelating General Relativity phenomenae with strongly coupled gauge theory physics.Comment: 35 pages, 3 figures. Lectures at the 5th Aegean summer school, `From gravity to thermal gauge theories: the AdS/CFT correspondence'. To appear in the proceedings in `Lecture Notes in Physics

Shockwaves and deep inelastic scattering within the gauge/gravity duality

Within the gauge/gravity correspondence, we discuss the general formulation of the shockwave metric which is dual to a 'nucleus' described by the strongly-coupled N=4 SYM theory in the limit where the number of colors Nc is arbitrarily large. We emphasize that the 'nucleus' must possess Nc^2 degrees of freedom per unit volume, so like a finite-temperature plasma, in order for a supergravity description to exist. We critically reassess previous proposals for introducing transverse inhomogeneity in the shockwave and formulate a new proposal in that sense, which involves no external source but requires the introduction of an 'infrared' cutoff which mimics confinement. This cutoff however plays no role when the shockwave is probed by a highly virtual projectile, so like in deep inelastic scattering. We consider two such projectiles, the dilaton and the R-current, and compute the respective structure functions including unitarity corrections. We find that there are no leading-twist contributions to the structure functions at high virtuality, meaning that there are no point-like constituents in the strongly coupled 'nucleus'. In the black-disk regime at low virtuality, the structure functions are suggestive of parton saturation with occupation numbers of order one. The saturation momentum Qs grows with the energy like Qs^2 ~ 1/x (with x the Bjorken variable), which is the hallmark of graviton exchanges and is also necessary for the fulfillment of the energy-momentum sum rules.Comment: 43 page