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

TL;DR

The paper addresses how to construct a celestial, infrared-safe observable that makes celestial conformal symmetry explicit in four-dimensional scattering. It defines the celestial Energy-Energy Correlator (cEEC) as a boost-eigenstate correlator of Average Null Energy operators, formulated on a Schwinger-Keldysh contour, and relates it to the full-range EEC via a moment integral that isolates lightray-transition contributions. At leading order, the authors compute the cEEC in $\mathcal{N}=8$ supergravity, Einstein gravity, $\mathcal{N}=4$ SYM, and pure YM; gravity results yield a compact closed form, while YM/SYM exhibit IR-divergent beam contributions requiring renormalization. In $\mathcal{N}=8$ SUGRA the cEEC is uniquely fixed by celestial symmetries and boundary data, illustrating a successful analytic bootstrap for celestial observables. The work establishes the cEEC as a unifying, infrared-safe observable that interpolates collinear, Sudakov, and Regge regimes, enabling new connections between celestial holography and collider phenomenology and motivating further bootstrap-based analyses.

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.

Figures (7)

• Figure 1: Schematic illustration of the operator definition of the cEEC on a Schwinger-Keldysh contour. The beam operators $\mathbb{P}_1^{J_1}$ and $\mathbb{P}_2^{J_2}$ prepare boost eigenstates as initial states, while the ANE operators $\mathcal{E}(n_a)$ and $\mathcal{E}(n_b)$ are inserted on the forward branch to measure energy flow in directions $n_a$ and $n_b$.
• Figure 2: Standard configuration of Eq. \ref{['eq: std configuration']}, with detector $b$ at an arbitrary point on the sphere.
• Figure 3: All information of the cEEC is contained in the upper half unit disc, with a direct physical interpretation.
• Figure 4: $\operatorname{cEEC}^{(0,0)}_{\text{SUGRA}}(z,\bar{z})$ on the celestial sphere. Detector $a$ is fixed at $(1,0,0)$, while the color map indicates the value of the cEEC as detector $b$ moves around the sphere.
• Figure 5: $\operatorname{cEEC}^{(0,0)}_{\text{SUGRA}}(z,\bar{z})$ on the upper half unit disc in the complex plane. One can clearly identify the Regge and away-side coplanar singularities, as well as the zero on positive real axis.