Celestial Energy-Energy Correlation in Yang-Mills Theory and Gravity

TL;DR

This paper introduces the Celestial Energy-Energy Correlator (cEEC), a new observable in gauge and gravity theories that reveals celestial conformal symmetry and interpolates between key perturbative regimes, with explicit computations in several theories.

Contribution

It defines the cEEC as a celestial conformal correlator, computes it in various theories, and demonstrates the power of celestial symmetries and bootstrap methods in determining its form.

Findings

cEEC is infrared and collinear safe.

Explicit first-order calculations in multiple theories.

Celestial symmetries determine cEEC in supergravity.

Abstract

We introduce the Celestial Energy-Energy Correlator (cEEC), an infrared and collinear safe observable that makes the celestial conformal symmetry of four-dimensional scattering manifest. The cEEC is defined as a correlation function of Average Null Energy operators measured on boost eigenstates, and takes the form of a four-point function in a fictitious two-dimensional CFT on the celestial sphere. An important feature of the cEEC is that it smoothly interpolates between different key regimes of perturbative gauge theory and gravity, such as the collinear limit, the Sudakov limit, and the Regge limit. We compute the cEEC to the first non-trivial order in $\mathcal{N}=4$ super Yang-Mills, pure Yang-Mills, Einstein gravity, and $\mathcal{N}=8$ supergravity. In $\mathcal{N}=8$ supergravity, the cEEC is uniquely determined by celestial symmetries and boundary data, demonstrating that bootstrap methods can yield closed-form results for this class of observables.