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

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.

💡 Research Summary

The paper introduces the Celestial Energy‑Energy Correlator (cEEC), a novel infrared‑ and collinear‑safe observable that makes the hidden conformal symmetry of four‑dimensional scattering manifest on the celestial sphere. The construction starts from the familiar Energy‑Energy Correlator (EEC), which measures the correlation of energy flow operators in a given final state, but replaces the usual momentum eigenstate initial condition with boost‑eigenstate operators (P^{(J)}(n)). These operators create states that are eigenvectors of Lorentz boosts along a chosen direction (n) with eigenvalue (J). By inserting two Average Null Energy (ANE) operators (E(n_a)) and (E(n_b)) on a Schwinger‑Keldysh contour and tracing over the product (E(n_a)E(n_b)P^{(J_1)}_1(n_1)P^{(J_2)}_2(n_2)), the authors define a four‑point function that depends only on the four null directions ({n_a,n_b,n_1,n_2}). In stereographic coordinates ((z,\bar z)) on the celestial sphere the correlator reduces to a function (G^{(J_1,J_2)}(u,v)) of the standard cross‑ratios (u=z\bar z) and (v=(1-z)(1-\bar z)). The boost eigenstate preparation eliminates the dependence on the auxiliary variable (\hat w) that appears in the ordinary EEC, leaving a simple overall power law ((n_1!\cdot! n_2)^{-(J_1+J_2)}). This mirrors the simplification seen in moments of parton distribution functions and guarantees infrared and collinear safety.

The authors compute the cEEC at the first non‑trivial order (tree‑level 2→5 scattering) in four theories: (\mathcal N=4) super‑Yang‑Mills (SYM), pure Yang‑Mills, Einstein gravity, and (\mathcal N=8) supergravity (SUGRA). The calculation proceeds by first evaluating the full‑range EEC, extracting the form factor (F(u,v,\hat w)), and then performing the rapidity integral that defines (G^{(J_1,J_2)}). In gravity the rapidity integral converges, while in gauge theories it diverges linearly, signalling the need for renormalization of the boost operators—an issue analogous to detector‑operator renormalization.

The most striking result appears in (\mathcal N=8) SUGRA. The cEEC takes a compact analytic form involving logarithms and dilogarithms: \