Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Energy Detectors and Asymptotic Symmetries

Hernán A. González, Jakob Salzer

TL;DR

The paper develops detector operators that measure energy flux at null infinity and shows they form a universal set under collinear factorization, yielding a closed leading OPE for generalized energy operators $\mathcal{E}^{[s]}_{\Delta}$ in both gravity and Yang–Mills theories. It identifies the $\Delta=2$ detector as the particle-number operator, and demonstrates that particle counting is not independent but is determined by soft charges, expressible as bilinears of conformally soft currents in gravity (via $P_z$) and in gauge theory (via soft currents $J_z,J_{ar z}$ and their shadows). The work connects detector observables to the soft sector of celestial holography, matching bulk collinear data with celestial OPEs and revealing a unified soft–detector structure that may hint at an underlying Celestial CFT organization. These results provide a concrete framework to study infrared physics, memory effects, and asymptotic symmetries through detectors on the celestial sphere and Carrollian boundary fields, with potential extensions to other detector observables and higher-point correlators.

Abstract

We study detector operators measuring energy to a power $Δ-2$ 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 $Δ=2$ 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.

Energy Detectors and Asymptotic Symmetries

TL;DR

The paper develops detector operators that measure energy flux at null infinity and shows they form a universal set under collinear factorization, yielding a closed leading OPE for generalized energy operators in both gravity and Yang–Mills theories. It identifies the detector as the particle-number operator, and demonstrates that particle counting is not independent but is determined by soft charges, expressible as bilinears of conformally soft currents in gravity (via ) and in gauge theory (via soft currents and their shadows). The work connects detector observables to the soft sector of celestial holography, matching bulk collinear data with celestial OPEs and revealing a unified soft–detector structure that may hint at an underlying Celestial CFT organization. These results provide a concrete framework to study infrared physics, memory effects, and asymptotic symmetries through detectors on the celestial sphere and Carrollian boundary fields, with potential extensions to other detector observables and higher-point correlators.

Abstract

We study detector operators measuring energy to a power 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 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 Kac-Moody soft currents. This work establishes thus a direct link between detector observables and the soft sector of celestial holography.

Paper Structure

This paper contains 18 sections, 95 equations.

Table of Contents

  1. Introduction
  2. Definition of generalized energy operators
  3. Building detector operators from Carrollian fields
  4. The generalized energy operator
  5. Detectors in the celestial basis
  6. Detector OPE from collinear limit
  7. Energy correlators and weighted cross-sections
  8. Detector OPE from collinear factorization
  9. Detector operators and celestial holography
  10. Detector OPE from celestial OPE
  11. The emergence of the number operator
  12. Detector correlators and soft properties
  13. The Delta=2 operator in gravity
  14. The Delta=2 operator in gauge theory
  15. Concluding remarks
  16. ...and 3 more sections