Abstract
Constructing charges in the covariant phase space formalism often leads to formally divergent expressions, even when the fields satisfy physically acceptable fall-off conditions. These expressions can be rendered finite by corner ambiguities in the definition of the presymplectic potential, which in some cases may be motivated by arguments involving boundary Lagrangians. We show that the necessary corner terms are already present in the variation of the bulk action and can be extracted in a straightforward way. Once these corner terms are included in the presymplectic potential, charges derived from an associated codimension-2 form are automatically finite. We illustrate the procedure with examples in two and three dimensions, working in Bondi gauge and obtaining integrable charges. As a by-product, actions are derived for these theories that admit a well-defined variational principle when the fields satisfy boundary conditions on a timelike surface with corners. An interesting feature of our analysis is that the fields are not required to be fully on-shell.
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Acknowledgments
The authors thank Adrien Fiorucci for helpful discussions and comments on a draft of this paper. We also thank Daniel Grumiller and Florian Ecker for stimulating conversations, and Technical University of Vienna for hospitality during the early stages of this project. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
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McNees, R., Zwikel, C. Finite charges from the bulk action. J. High Energ. Phys. 2023, 154 (2023). https://doi.org/10.1007/JHEP08(2023)154
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DOI: https://doi.org/10.1007/JHEP08(2023)154