Abstract

Abstract Recent studies, using the AdS/CFT correspondence, of the radiation produced by a decaying system or by an accelerated charge in the $ \mathcal{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 $ \mathcal{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.

Highlights

  • Pattern as in the corresponding problems at zero coupling: the radiation appears to propagate at the speed of light, without any trace of quantum broadening

  • 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 generic: it holds in any field theory with non-trivial interactions

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Summary

Preliminaries: observables for decaying states

We expect a three-point function to be a good measurement (say, of the energy) when ∆+ ≪ γ2/τ — in which case it correctly provides the energy density per unit transverse area (or per unit solid angle in the photon rest frame) —, but not in the opposite case (∆+ γ2/τ ), where the longitudinal resolution is relatively high. These expectations will be confirmed by the subsequent calculations, at both strong and weak coupling

The three-point function at infinitely strong coupling
Backreaction in supergravity
A physical interpretation for the ‘backreaction’
Momentum-space analysis of the backreaction
The three-point function at zero coupling
The decay rate
The three-point function
Jet evolution at weak coupling but late time
The general picture
The four-point function and deep inelastic scattering
Witten diagrams at strong coupling
Preliminaries: bulk excitations
The three- and four-point functions
Physical discussion
A The EB term for the falling particle
B Fragmentation function at strong coupling
Full Text
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