193 research outputs found
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 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
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