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<p>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 <i>S</i>-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 <i>SU</i> (<i>N</i>) Kac-Moody soft currents. This work thus establishes a direct link between detector observables and the soft sector of celestial holography.</p>

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Energy detectors and asymptotic symmetries

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月27日

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  • Hernán A. González,
  • Jakob Salzer

摘要

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.