21,260 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
High energy Scattering in 2+1 QCD: A Dipole Picture
A dipole picture of high energy scattering is developed in the 2+1
dimensional QCD, following Mueller. A generalized integral equation for the
dipole density with a given separation and center of mass position is derived,
and meson-meson non-forward scattering amplitude is therefore calculated. We
also calculate the amplitude due to two pomeron exchange, and the triple
pomeron coupling. We compare the result obtained by this method to our previous
result based on an effective action approach, and find the two results agree at
the one pomeron exchange level.Comment: minor typos corrected. Postscript files are available through
anonymous ftp quark.het.brown.edu, in the directory /pub/preprints, file name
is 9407299. Hard copy is available upon reques
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