88 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
3d Modularity
We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d
theories where such structures a priori are not manifest. These modular
structures include: mock modular forms, Weil
representations, quantum modular forms, non-semisimple modular tensor
categories, and chiral algebras of logarithmic CFTs.Comment: 119 pages, 10 figures and 20 table
The Asymptotic Couple of the Field of Logarithmic Transseries
The derivation on the differential-valued field of
logarithmic transseries induces on its value group a certain
map . The structure is a divisible asymptotic
couple. We prove that the theory
admits elimination of quantifiers in a natural first-order language. All models
of have an important discrete subset
. We give explicit descriptions of all
definable functions on and prove that is stably embedded in
.Comment: 24 page
Integration on the Surreals
Conway's real closed field No of surreal numbers is a sweeping generalization
of the real numbers and the ordinals to which a number of elementary functions
such as log and exponentiation have been shown to extend. The problems of
identifying significant classes of functions that can be so extended and of
defining integration for them have proven to be formidable. In this paper, we
address this and related unresolved issues by showing that extensions to No,
and thereby integrals, exist for most functions arising in practical
applications. In particular, we show they exist for a large subclass of the
resurgent functions, a subclass that contains the functions that at infinity
are semi-algebraic, semi-analytic, analytic, meromorphic, and Borel summable as
well as generic solutions to linear and nonlinear systems of ODEs possibly
having irregular singularities. We further establish a sufficient condition for
the theory to carry over to ordered exponential subfields of No more generally
and illustrate the result with structures familiar from the surreal literature.
We work in NBG less the Axiom of Choice (for both sets and proper classes),
with the result that the extensions of functions and integrals that concern us
here have a "constructive" nature in this sense. In the Appendix it is shown
that the existence of such constructive extensions and integrals of
substantially more general types of functions (e.g. smooth functions) is
obstructed by considerations from the foundations of mathematics.Comment: This paper supersedes the positive portion of O. Costin, P. Ehrlich
and H. Friedman, "Integration on the surreals: a conjecture of Conway,
Kruskal and Norton", arXiv:1505.02478v3, 24 Aug 2015. A separate paper
superseding the negative portion of the earlier arXiv preprint is in
preparation by H. Friedman and O. Costi
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