On the dispersion of fundamental particles in QCD and N=4 Super Yang-Mills theory

We study thermal corrections to the dispersion relations of massive fundamental particles immersed in weakly coupled non-Abelian plasmas. The cases covered include quarks in the QCD (quark-gluon) plasma, as well as N=2 quarks and scalars in an N=4 Super Yang-Mills plasma. We perform the calculations to leading order in a weak coupling expansion, and consider all mass scales of the fundamental fields, ranging from massless particles all the way to bare masses parametrically larger than the temperature.Comment: 41 pages, 8 figures; v2 to be published in JHEP, with one table added to summarize result

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

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

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

Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD

Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.Comment: 22 pages. v2: a reference and clarifications added; published versio

Comparing different freeze-out scenarios in azimuthal hadron correlations induced by fast partons

I review the linearized hydrodynamical treatment of a fast parton traversing a perturbative quark-gluon plasma. Using numerical solutions for the medium's response to the fast parton, I obtain the medium's distribution function which is then used in a Cooper-Frye freeze-out prescription to obtain an azimuthal particle spectrum. Two different freeze-out scenarios are considered which yield significantly different results. I conclude that any meaningful comparison of azimuthal hadron correlation functions to RHIC data requires implementing a realistic freeze-out scenario in an expanding medium.Comment: Contribution to the Proceedings for 2008 Hot Quarks in Estes Park, CO, as accepted for publication in EPJ-

Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order

We present the full details of a calculation at next-to-leading order of the momentum diffusion coefficient of a heavy quark in a hot, weakly coupled, QCD plasma. Corrections arise at O(g_s); physically they represent interference between overlapping scatterings, as well as soft, electric scale (p ~ gT) gauge field physics, which we treat using the hard thermal loop (HTL) effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at NLO is kappa = (16\pi/3) alpha_s^2 T^3 (log(1/g) + 0.07428 + 1.9026 g). We extend the computation to a heavy fundamental representation ``probe'' quark in large N_c, N=4 Super Yang-Mills theory, where the result is kappa^{SYM}= (lambda^2 T^3)(6\pi) (log(1/\sqrt{\lambda}) + 0.4304 + 0.8010 \sqrt{lambda}) (where lambda=g_s^2 N_c is the t'Hooft coupling). In the absence of some resummation technique, the convergence of perturbation theory is poor.Comment: 40 pages, 14 figure

Remarks on Heavy-Light Mesons from AdS/CFT

We use the AdS/CFT correspondence to compute the energy spectrum of heavy-light mesons in a N=2 SU(N) super Yang-Mills theory with two massive hypermultiplets. In the heavy quark limit, similar to QCD, we find that the excitation energies are independent of the heavy quark mass. We also make some remarks about related AdS/CFT models of flavor with less supersymmetry.Comment: 29 pages, 9 figures; v2 section 5 rewritten to include discussion of long strings, other minor improvements, ref adde

The Energy of a Moving Quark-Antiquark Pair in an N=4 SYM Plasma

We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal N=4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or gamma/L) behavior at small quark-antiquark separations, and becomes unbound beyond a certain screening length whose velocity-dependence we determine. We discuss the relation between the high-velocity limit of our results and the lightlike Wilson loop proposed recently as a definition of the jet-quenching parameter.Comment: LaTeX 2e, 27 pages, 8 eps figures; v2: added computation of the pair energy in the plasma rest frame, clarified the comparison with hep-ph/0607062, corrected typos, added reference

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