Energy Detectors, OPEs and Soft Modes in Asymptotically Flat Gravity

Abstract

In this talk, we analyze detector operators that measure energy to the power ∆-2 at null infinity in Einstein gravity. These operators transform as conformal primaries on the celestial sphere and provide a natural basis for describing energy-flux observables in scattering processes. Using the collinear factorization of scattering amplitudes, we derive the universal leading structure of the operator product expansion (OPE). A key consequence of our analysis is the precise identification of the ∆=2 detector, the number operator. Exploiting the fact that soft charges generate symmetries of the S-matrix, we demonstrate that the number of particles is entirely determined by the product of two supertranslation currents. This work establishes a direct link between detector observables and the soft sector of celestial holography. Analogous conclusions hold for Yang–Mills theory.