Energy Detectors and Asymptotic Symmetries

Abstract

We study detector operators measuring energy to a power $\Delta-2$ at null infinity in four-dimensional gauge theories and 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. A key consequence of our analysis is the precise identification of the $\Delta=2$ 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 soft currents: in gravity, the operator is the square of the supertranslation generator, while in Yang-Mills yields a product of $SU(N)$ Kac-Moody soft currents. This work establishes thus a direct link between detector observables and the soft sector of celestial holography.