Light-ray operators, detectors and gravitational event shapes

Abstract

Light-ray operators naturally arise from integrating Einstein equations at null infinity along the light-cone time. We associate light-ray operators to physical detectors on the celestial sphere and we provide explicit expressions in perturbation theory for their hard modes using the steepest descent technique. We then study their algebra in generic 4-dimensional QFTs of massless particles with integer spin, comparing with complexified Cordova-Shao algebra. For the case of gravity, the Bondi news squared term provides an extension of the ANEC operator at infinity to a shear-inclusive ANEC, which as a quantum operator gives the energy of all quanta of radiation in a particular direction on the sky. We finally provide a direct connection of the action of the shear-inclusive ANEC with detector event shapes and we study infrared-safe gravitational wave event shapes produced in the scattering of massive compact objects, computing the energy flux at infinity in the classical limit at leading order in the soft expansion.

Graviton particle statistics and coherent states from classical scattering amplitudes

“…There it was shown that a Poissonian distribution of the cut reggeons naturally explain the AGK cancellation, and this actually inspired part of the ideas developed in this work. Furthermore, the set of infinite amplitude relations we found must have some nontrivial overlap with the ones related to soft theorems [37,97], which in general are also valid beyond the classical regime. It would be interesting to explore this further.…”

“…This is crucial to obtain a well-behaved scattering angle at high energies [33], as was proven by a direct calculation of radiation reaction effects [11,12,[34][35][36]. A similar principle holds as well for less inclusive observables like gravitational energy event shapes [37]. 1 We would like to understand the exact structure of the final semiclassical state, including classical radiation.…”

“…From the pure amplitude perspective, the same question is hard to answer unless we work strictly in the soft approximation [37,49,52]. But in general, we can address this question perturbatively by looking at the mean and the variance of the particle distribution.…”

“…Indeed, the contribution of zero-energy gravitons to the final state, which give rise to the infrared divergent contributions, is known to be exactly represented by a coherent state. This can be proved either from a Faddeev-Kulish approach [37,52] or from a path integral perspective [40,42,55]. Let us denote the mean and the variance of this coherent state for zero-energy gravitons by µ E k ∼0 out and Σ E k ∼0 out respectively.…”

“…Indeed, a very simple explanation of this fact in the case of "power-suppressed" observables in gravity is given by the invariance under BMS soft supertranslations, i.e. the invariance under the addition of an arbitrary number of soft gravitons[37][38][39].2 See however[52] for a notable exception at the leading order in the soft expansion.…”