  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.
