Energy correlators in four-dimensional gravity

TL;DR

This paper analyzes energy correlators in four-dimensional gravity, demonstrating infrared finiteness, universality in soft-graviton dynamics, and exploring their analytic properties and singularities across various gravitational theories.

Contribution

It provides explicit one-loop calculations of energy correlators in supergravity and Einstein gravity, derives all-order expressions in the back-to-back limit, and introduces a simple beam-averaged correlator with dispersion relations.

Findings

Infrared divergences cancel in energy correlators.

Energy-energy correlator governed by universal soft-graviton dynamics.

Gravitational correlators exhibit unique singularities from long-range interactions.

Abstract

We investigate energy correlators in four-dimensional gravitational theories, which provide a simple class of infrared-finite observables. We compute the one- and two-point energy correlators at one loop in $\mathcal{N}=8$ supergravity and in pure Einstein gravity, with particular emphasis on the contact terms arising from the interplay between virtual corrections and real emissions. We explicitly demonstrate the cancellation of infrared divergences and verify the Ward identities associated with energy-momentum conservation. In the back-to-back limit, we derive an all-order expression for the energy-energy correlator, showing that it is governed by universal soft-graviton dynamics. We further introduce a particularly simple beam-averaged energy-energy correlator and compute it in different gravitational theories, including tree-level string theory. The resulting correlators exhibit analyticity and polynomial boundedness, allowing for the formulation of dispersion relations, which we explore. Finally, we discuss additional singularities of the gravitational energy correlators, absent in QCD, that originate from the long-range nature of the gravitational interactions.