The Hydrodynamics of M-Theory

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets [hep-th/0205051]. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.Comment: 1+19 pages, references added, section 5 clarified, eq. (72) correcte

Transport coefficients, membrane couplings and universality at extremality

We present an efficient method for computing the zero frequency limit of transport coefficients in strongly coupled field theories described holographically by higher derivative gravity theories. Hydrodynamic parameters such as shear viscosity and conductivity can be obtained by computing residues of poles of the off-shell lagrangian density. We clarify in which sense these coefficients can be thought of as effective couplings at the horizon, and present analytic, Wald-like formulae for the shear viscosity and conductivity in a large class of general higher derivative lagrangians. We show how to apply our methods to systems at zero temperature but finite chemical potential. Our results imply that such theories satisfy $\eta/s=1/4\pi$ universally in the Einstein-Maxwell sector. Likewise, the zero frequency limit of the real part of the conductivity for such systems is shown to be universally zero, and we conjecture that higher derivative corrections in this sector do not modify this result to all orders in perturbation theory.Comment: 29 pages, v2: Small text changes for clarity, typos correcte

String Theory and Quantum Chromodynamics

I review recent progress on the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics covered include the large-Nc limit of gauge theories, the gravitational description of gauge theory thermodynamics and hydrodynamics, and confinement/deconfinement thermal phase transitions.Comment: 38 pages, 24 figures. Lectures given at the RTN Winter School on "Strings, Supergravity and Gauge Theories" at CERN on January 15-19, 200

The Second Sound of SU(2)

Using the AdS/CFT correspondence, we calculate the transport coefficients of a strongly interacting system with a non-abelian SU(2) global symmetry near a second order phase transition. From the behavior of the poles in the Green's functions near the phase transition, we determine analytically the speed of second sound, the conductivity, and diffusion constants. We discuss similarities and differences between this and other systems with vector order parameters such as p-wave superconductors and liquid helium-3.Comment: 31 pages, 2 figures; v2 ref added, typo fixe

The Energy Loss of a Heavy Quark Moving in a Viscous Fluid

To study the rate of energy and momentum loss of a heavy quark in QGP, specifically in the hydrodynamic regime, we use fluid/gravity duality and construct a perturbative procedure to find the string solution in gravity side. We show that by this construction the drag force exerted on the quark can be computed perturbatively, order by order in a boundary derivative expansion. At ideal order, our result is just the drag force exerted on a moving quark in thermal plasma with thermodynamics variables promoted to become local functions of space and time. Furthermore, we apply this procedure to a transverse quark in Bjorken flow and compute the first-derivative corrections, namely the viscous corrections, to the drag force.Comment: 33 pages, 6 figures, references added v5: Some correction

Properties of some conformal field theories with M-theory duals

By studying classes of supersymmetric solutions of D=11 supergravity with AdS_5 factors, we determine some properties of the dual four-dimensional N=1 superconformal field theories. For some explicit solutions we calculate the central charges and also the conformal dimensions of certain chiral primary operators arising from wrapped membranes. For the most general class of solutions we show that there is a consistent Kaluza-Klein truncation to minimal D=5 gauged supergravity. This latter result allows us to study some aspects of the dual strongly coupled thermal plasma with a non-zero R-charge chemical potential and, in particular, we show that the ratio of the shear viscosity to the entropy density has the universal value of 1/4 pi.Comment: Consistent truncation extended to include fermions. Reference added. 28 page

Shear Viscosity in the O(N) Model

We compute the shear viscosity in the O(N) model at first nontrivial order in the large N expansion. The calculation is organized using the 1/N expansion of the 2PI effective action (2PI-1/N expansion) to next-to-leading order, which leads to an integral equation summing ladder and bubble diagrams. We also consider the weakly coupled theory for arbitrary N, using the three-loop expansion of the 2PI effective action. In the limit of weak coupling and vanishing mass, we find an approximate analytical solution of the integral equation. For general coupling and mass, the integral equation is solved numerically using a variational approach. The shear viscosity turns out to be close to the result obtained in the weak-coupling analysis.Comment: 37 pages, few typos corrected; to appear in JHE

Hydrodynamics of fundamental matter

First and second order transport coefficients are calculated for the strongly coupled N=4 SYM plasma coupled to massless fundamental matter in the Veneziano limit. The results, including among others the value of the bulk viscosity and some relaxation times, are presented at next-to-leading order in the flavor contribution. The bulk viscosity is found to saturate Buchel's bound. This result is also captured by an effective single-scalar five-dimensional holographic dual in the Chamblin-Reall class and it is suggested to hold, in the limit of small deformations, for generic plasmas with gravity duals, whenever the leading conformality breaking effects are driven by marginally (ir)relevant operators. This proposal is then extended to other relations for hydrodynamic coefficients, which are conjectured to be universal for every non-conformal plasma with a dual Chamblin-Reall-like description. Our analysis extends to any strongly coupled gauge theory describing the low energy dynamics of Nc>>1 D3-branes at the tip of a generic Calabi-Yau cone. The fundamental fields are added by means of 1<<Nf<<Nc homogeneously smeared D7-branes.Comment: 24 pages. V2: Important improvements in the discussion of the results in section 1. References adde

An Introduction to the Covariant Quantization of Superstrings

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green--Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by others. In the appendices, we include some background material for the Green-Schwarz and Berkovits formulations, in order that this presentation be self contained.Comment: LaTex, 23 pp. Contribution to the Proceedings of the Workshop in String Theory, Leuven 2002, some references added and a comment on ref. [16

Aspects of higher curvature terms and U-duality

We discuss various aspects of dimensional reduction of gravity with the Einstein-Hilbert action supplemented by a lowest order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R^2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially SL(n+1,Z) for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R^3 and R^4 by calculating some terms relevant for the coset formulation, aiming in particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an investigation of the derivative structure. We emphasise some issues concerning the need for the introduction of non-scalar automorphic forms in order to realise certain expected enhanced symmetries.Comment: 26 pp., 15 figs., plain te