We would like to thank Laurent Freidel, Prahar Mitra, and Andrew Strominger for enlightening discussions, and especially Laurent Freidel for comments on a draft. T H and K Z are supported by the Heising-Simons Foundation 'Observational Signatures of Quantum Gravity' collaboration Grant 2021-2817, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and the Walter Burke Institute for Theoretical Physics. A.R. has been supported in part by a Heising-Simons postdoctoral fellowship Grant 2021-2817 and a Marie Curie fellowship Grant Agreement 101063234 at the University of Amsterdam, as well as the Simons Foundation through the Emmy Noether Fellows Program at Perimeter Institute (1034867, Dittrich). A R is grateful for the hospitality of Perimeter Institute where part of this work was carried out. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. The work of K Z is also supported by a Simons Investigator award.
An infrared on-shell action and its implications for soft charge fluctuations in asymptotically flat spacetimes
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1.
California Institute of Technology
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2.
King's College London
Abstract
We study the infrared on-shell action of Einstein gravity in asymptotically flat spacetimes (AFSs), obtaining an effective, gauge-invariant boundary action for memory and shockwave spacetimes. We show that the phase space is in both cases parameterized by the leading soft variables in AFSs, thereby extending the equivalence between shockwave and soft commutators to spacetimes with non-vanishing Bondi mass. We then demonstrate that our on-shell action is equal to three quantities studied separately in the literature: (i) the soft supertranslation charge; (ii) the shockwave effective action, or equivalently the modular Hamiltonian; and (iii) the soft effective action. Finally, we compute the quantum fluctuations in the soft supertranslation charge and, assuming the supertranslation parameter may be promoted to an operator, we obtain an area law, consistent with earlier results showing that the modular Hamiltonian has such fluctuations.
Copyright and License
© 2025 The Author(s). Published by IOP Publishing Ltd.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Acknowledgement
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Additional details
- Heising-Simons Foundation
- 2021-2817
- United States Department of Energy
- DE-SC0011632
- HORIZON EUROPE Marie Sklodowska-Curie Actions
- 101063234
- Simons Foundation
- 1034867
- Accepted
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2025-03-24
- Caltech groups
- Walter Burke Institute for Theoretical Physics, Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- Published