Energy detectors and asymptotic symmetries

A bstract We study detector operators measuring energy to a power ∆ – 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 ∆ = 2 detector with the particle-number operator. Exploiting the fact that soft charges generate symmetries of the S -matrix, we show that the residue of the number operator, evaluated on scattering states, can be represented in terms of bilinears of conformally soft currents: in gravity, the operator is the square of the supertranslation generator, while in Yang-Mills it yields a product of SU ( N ) Kac-Moody soft currents. This work thus establishes a direct link between detector observables and the soft sector of celestial holography.