39 research outputs found
Universal behaviour, transients and attractors in supersymmetric Yang-Mills plasma
Numerical simulations of expanding plasma based on the AdS/CFT correspondence
as well as kinetic theory and hydrodynamic models strongly suggest that some
observables exhibit universal behaviour even when the system is not close to
local equilibrium. This leading behaviour is expected to be corrected by
transient, exponentially decaying contributions which carry information about
the initial state. Focusing on late times, when the system is already in the
hydrodynamic regime, we analyse numerical solutions describing expanding plasma
of strongly coupled N=4 supersymmetric Yang-Mills theory and identify these
transient effects, matching them in a quantitative way to leading trans-series
corrections corresponding to least-damped quasinormal modes of AdS black
branes. In the process we offer additional evidence supporting the recent
identification of the Borel sum of the hydrodynamic gradient expansion with the
far-from-equilibrium attractor in this system.Comment: Introduction improved, additional reference
On the hydrodynamic attractor of Yang-Mills plasma
There is mounting evidence suggesting that relativistic hydrodynamics becomes
relevant for the physics of quark-gluon plasma as the result of nonhydrodynamic
modes decaying to an attractor apparent even when the system is far from local
equilibrium. Here we determine this attractor for Bjorken flow in N=4
supersymmetric Yang-Mills theory using Borel summation of the gradient
expansion of the expectation value of the energy momentum tensor. By comparing
the result to numerical simulations of the flow based on the AdS/CFT
correspondence we show that it provides an accurate and unambiguous
approximation of the hydrodynamic attractor in this system. This development
has important implications for the formulation of effective theories of
hydrodynamics.Comment: 6 pages, 4 figures. v2: many small improvements. v3: introduction
rephrased to emphasise key point
QGP Physics from Attractor Perturbations
The strong longitudinal expansion characteristic of heavy-ion collisions
leads to universal attractor behaviour of the resulting drop of Quark-Gluon
Plasma already at very early times. Assuming approximate boost invariance, we
incorporate transverse dynamics of this system by linearizing the
Mueller-Israel-Stewart theory around the attractor. The result is a system of
coupled ordinary differential equations which describe the proper-time
evolution of Fourier modes encoding the transverse structure of the initial
energy deposition. The late time asymptotic behaviour of solutions is described
by transseries which make manifest the stability of the attractor against
transverse perturbations. In this framework, most of the physically relevant
information resides in the exponentially suppressed corrections to evolution
along the attractor, which are not yet negligible at freeze-out. These findings
also suggest a simple numerical approach to QGP dynamics which accounts for the
transverse dynamics using a finite number of Fourier modes. We show that this
approach is able to describe collectivity at the level of the transverse
anisotropy, as a surrogate for elliptic flow. Physical observables can be
expressed in terms of the asymptotic data evaluated at freeze-out, which we
illustrate by calculating the final multiplicity distributions.Comment: 15 pages, 7 figure
Transient Relativistic Fluid Dynamics in a General Hydrodynamic Frame
We propose a new theory of second-order viscous relativistic hydrodynamics
which does not impose any frame conditions on the choice of the hydrodynamic
variables. It differs from Mueller-Israel-Stewart theory by including
additional transient degrees of freedom, and its first-order truncation reduces
to Bemfica-Disconzi-Noronha-Kovtun theory. Conditions for causality and
stability are explicitly given in the conformal regime. As an illustrative
example, we consider Bjorken flow solutions to our equations and identify
variables which make a hydrodynamic attractor manifest.Comment: 10 pages, 1 figure, version accepted for publication in Physical
Review Letter
Generalized string compactifications with spontaneously broken supersymmetry
The Narain lattice construction of string compactifications is generalized to
include spontaneously broken supersymmetry. Consistency conditions from modular
invariance and Lorentz symmetry are solved in full generality. This framework
incorporates models where supersymmetry breaking is inversely proportional to
the radii of compact dimensions. The enhanced lattice description, however,
might allow for models with a different geometrical or even non-geometrical
interpretation.Comment: 15 pages, LaTeX, no figure
Some half-BPS solutions of M-theory
It was recently shown that half BPS-solutions of M-theory can be expressed in
terms of a single function satisfying the 3-d continuum Toda equation. In this
note half-BPS solutions corresponding to separable solutions of the Toda
equations are examined.Comment: Typos fixed, reference adde
Branes and Fluxes in D=5 Calabi-Yau Compactifications of M-Theory
We discuss Poincare three-brane solutions in D=5 M-Theory compactifications
on Calabi-Yau (CY) threefolds with G-fluxes. We show that the vector moduli
freeze at an attractor point. In the case with background flux only, the
spacetime geometry contains a zero volume singularity with the three-brane and
the CY space shrinking simultaneously to a point. This problem can be avoided
by including explicit three-brane sources. We consider two cases in detail: a
single brane and, when the transverse dimension is compactified on a circle, a
pair of branes with opposite tensions.Comment: 14 pages, final versio
Rigorous bounds on transport from causality
We use causality to derive a number of simple and universal constraints on
dispersion relations, which describe the location of singularities of retarded
two-point functions in relativistic quantum field theories. We prove that all
causal dissipative dispersion relations have a finite radius of convergence. We
then give two-sided bounds on all transport coefficients in units of this
radius, including an upper bound on diffusivity.Comment: 4 pages. New relational bound on sound attenuation, improved test
function, references adde
Transseries for causal diffusive systems
The large proper-time behaviour of expanding boost-invariant fluids has
provided many crucial insights into quark-gluon plasma dynamics. Here we
formulate and explore the late-time behaviour of nonequilibrium dynamics at the
level of linearized perturbations of equilibrium, but without any special
symmetry assumptions. We introduce a useful quantitative approximation scheme
in which hydrodynamic modes appear as perturbative contributions while
transients are nonperturbative. In this way, solutions are naturally organized
into transseries as they are in the case of boost-invariant flows. We focus our
attention on the ubiquitous telegrapher's equation, the simplest example of a
causal theory with a hydrodynamic sector. In position space we uncover novel
transient contributions as well as Stokes phenomena which change the structure
of the transseries based on the spacetime region or the choice of initial data.Comment: 23 pages + appendices, 16 figure