Abstract
This paper presents a systematic cataloging of the generators of celestial symmetries on phase space. Starting from the celestial OPEs, we first show how to extract a representation of the general-spin analog of the wedge subalgebra of w1+∞ on the phase space of massless matter fields of arbitrary helicity. These generators can be expressed as light-sheet operators that are quadratic in the matter fields at future or past null infinity. We next show how to extend these symmetries beyond the wedge. Doing so requires us to augment the quadratic operators with: 1) linear terms corresponding to primary descendants of the negative helicity gauge fields the matter modes couple to, and 2) a tower of higher-particle composite operator contributions. These modes can be realized as light-ray operators supported on generators of null infinity, but local on the celestial sphere. Finally, we construct a representation of the celestial symmetries that captures how the positive helicity gauge fields transform. We close by discussing how these celestial symmetries inform our choice of detector operators.
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Acknowledgments
We would like to thank Luca Ciambelli, Joaquim Gomis, Mina Himwich, and especially Laurent Freidel for many useful conversations. The research of YH and SP is supported by the Celestial Holography Initiative at the Perimeter Institute for Theoretical Physics. This research program is supported by the Simons Collaboration on Celestial Holography. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
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Hu, Y., Pasterski, S. Detector operators for celestial symmetries. J. High Energ. Phys. 2023, 35 (2023). https://doi.org/10.1007/JHEP12(2023)035
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DOI: https://doi.org/10.1007/JHEP12(2023)035