174 research outputs found
The Boltzmann Equation in Classical Yang-Mills Theory
We give a detailed derivation of the Boltzmann equation, and in particular
its collision integral, in classical field theory. We first carry this out in a
scalar theory with both cubic and quartic interactions and subsequently in a
Yang-Mills theory. Our method is not relied on a doubling of the fields, rather
it is based on a diagrammatic approach representing the classical solution to
the problem.Comment: 24 pages, 7 figures; v2: typos corrected, reference added, published
in Eur. Phys. J.
Jet evolution from weak to strong coupling
Recent studies, using the AdS/CFT correspondence, of the radiation produced
by a decaying system or by an accelerated charge in the N=4 supersymmetric
Yang-Mills theory, led to a striking result: the 'supergravity backreaction',
which is supposed to describe the energy density at infinitely strong coupling,
yields exactly the same result as at zero coupling, that is, it shows no trace
of quantum broadening. We argue that this is not a real property of the
radiation at strong coupling, but an artifact of the backreaction calculation,
which is unable to faithfully capture the space-time distribution of the
radiation. This becomes obvious in the case of a decaying system ('virtual
photon'), for which the backreaction is tantamount to computing a three-point
function in the conformal gauge theory, which is independent of the coupling
since protected by symmetries. Whereas this non-renormalization property is
specific to the conformal N=4 SYM theory, we argue that the failure of the
three-point function to provide a local measurement is in fact generic: it
holds in any field theory with non-trivial interactions. To properly study a
localized distribution, one should rather compute a four-point function, as
standard in deep inelastic scattering. We substantiate these considerations
with studies of the radiation produced by the decay of a time-like photon at
both weak and strong coupling. We show that by computing four-point functions,
in perturbation theory at weak coupling and, respectively, from Witten diagrams
at strong coupling, one can follow the quantum evolution and thus demonstrate
the broadening of the energy distribution. This broadening is slow when the
coupling is weak but it proceeds as fast as possible in the limit of a strong
coupling.Comment: 49 pages, 6 figure
Resumming large higher-order corrections in non-linear QCD evolution
Linear and non-linear QCD evolutions at high energy suffer from severe issues
related to convergence, due to higher order corrections enhanced by large
double and single transverse logarithms. We resum double logarithms to all
orders by taking into account successive soft gluon emissions strongly ordered
in lifetime. We further resum single logarithms generated by the first
non-singular part of the splitting functions and by the one-loop running of the
coupling. The resulting collinearly improved BK equation admits stable
solutions, which are used to successfully fit the HERA data at small-x for
physically acceptable initial conditions and reasonable values of the fit
parameters.Comment: 4 pages, 4 figures, based on talk given at Hard Probes 2015, 29 June
- 3 July 2015, Montreal, Canad
Resummation of Large Logarithms in the Rapidity Evolution of Color Dipoles
Perturbative corrections beyond leading-log accuracy to BFKL and BK
equations, describing the rapidity evolution of QCD scattering amplitudes at
high energy, exhibit strong convergence problems due to radiative corrections
enhanced by large single and double transverse logs. We identify explicitly the
physical origin of double transverse logs and resum them directly in coordinate
space as appropriate for BK equation, in terms of an improved local-in-rapidity
evolution kernel. Numerical results show the crucial role of double-logarithmic
resummation for BK evolution, which is stabilized and slowed down by roughly a
factor of two.Comment: 6 pages, 4 figures; Proceedings of the XXIII International Workshop
on Deep-Inelastic Scattering (27 April-May 1 2015, Dallas (USA)
Aspects of the UV/IR correspondence : energy broadening and string fluctuations
We show that a source which radiates in the vacuum of the strongly coupled
N=4 SYM theory produces an energy distribution which, in the supergravity
approximation, has the same space-time pattern as the corresponding classical
distribution: the radiation propagates at the speed of light without
broadening. We illustrate this on the basis of several examples: a small
perturbation propagating down a steady string, a massless particle falling into
AdS_5, and the decay of a time-like wave-packet. A similar observation was made
in Phys. Rev. D81 (2010) 126001 for the case of a rotating string. In all these
cases, the absence of broadening is related to the fact that the energy
backreaction on the boundary arises exclusively from the bulk perturbation at,
or near, the boundary. This is so since bulk sources which propagate in AdS_5
at the speed of light do not generate any energy on the boundary. We interpret
these features as an artifact of the supergravity approximation, which fails to
encode quantum mechanical fluctuations that should be present even in the
strong coupling limit. We argue that such fluctuations should enter the dual
string theory as longitudinal string fluctuations, which are not suppressed at
strong coupling. We heuristically estimate the effects of such fluctuations and
argue that they restore the broadening of the radiation, in agreement with
expectations from both quantum mechanics and the ultraviolet/infrared
correspondence.Comment: 47 page
First correction to JIMWLK evolution from the classical equations of motion
We calculate some corrections to the JIMWLK kernel in
the framework of the light-cone wave function approach to the high energy limit
of QCD. The contributions that we consider originate from higher order
corrections in the strong coupling and in the density of the projectile to the
solution of the classical Yang-Mills equations of motion that determine the
Weizs\"acker-Williams fields of the projectile. We study the structure of these
corrections in the dipole limit, showing that they are subleading in the limit
of large number of colours , and that they cannot be fully recast in the
form of dipole degrees of freedom.Comment: 4 pages, LaTeX, 2 eps figures included using graphicx, uses enclosed
iopart.cls; contribution to the proceedings of Quark Matter 2006 (Shanghai,
November 14th-20th 2006
Schwarzschild-like solutions in Finsler-Randers gravity
In this work, we extend for the first time the spherically symmetric
Schwarzschild and Schwarzschild-De Sitter solutions with a Finsler-Randers-type
perturbation which is generated by a covector . This gives a locally
anisotropic character to the metric and induces a deviation from the Riemannian
models of gravity. A natural framework for this study is the Lorentz tangent
bundle of a spacetime manifold. We apply the generalized field equations to the
perturbed metric and derive the dynamics for the covector . Finally,
we find the timelike, spacelike and null paths on the Schwarzschild-Randers
spacetime, we solve the timelike ones numerically and we compare them with the
classic geodesics of general relativity. The obtained solutions are new and
they enrich the corresponding literature.Comment: 13 pages, 2 figures, to be published in EPJ
Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR)
spacetime previously investigated by a subset of the present authors
(Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis et al.
in Eur Phys J C 81(11):990, 2021). We will examine the dynamical analysis of
geodesics which provides the derivation of the energy and the angular momentum
of a particle moving along a geodesic of SFR spacetime. This study allows us to
compare our model with the corresponding of general relativity (GR). In
addition, the effective potential of SFR model is examined and it is compared
with the effective potential of GR. The phase portraits generated by these
effective potentials are also compared. Finally we deal with the derivation of
the deflection angle of the SFR spacetime and we find that there is a small
perturbation from the deflection angle of GR. We also derive an interesting
relation between the deflection angles of SFR model and the corresponding
result in the work of Shapiro et al (Phys Rev Lett 92(12):121101, 2004). These
small differences are attributed to the anisotropic metric structure of the
model and especially to a Randers term which provides a small deviation from
the GR.Comment: 21 pages, 5 figure
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