Aspects of the UV/IR correspondence : energy broadening and string fluctuations

TL;DR

The paper investigates how classical supergravity approximations in AdS/CFT correspondence fail to account for quantum fluctuations, leading to non-broadening energy distributions, and suggests that string fluctuations restore expected broadening effects.

Contribution

It demonstrates that classical supergravity predicts no energy broadening in radiation, and proposes that quantum string fluctuations are necessary to recover realistic broadening effects.

Findings

Supergravity predicts no energy broadening in radiation.

Quantum string fluctuations are expected to restore broadening.

Classical sources in AdS do not produce boundary energy spread.

Abstract

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.