Abstract
We show that the non-linear BMS5 symmetry algebra of asymptotically flat Einstein gravity in five dimensions, as well as the super-BMS4 superalgebra of asymptotically flat supergravity, can be redefined so as to take a direct sum structure. In the new presentation of the (super-)algebra, angle-dependent translations and angle-dependent supersymmetry transformations commute with the (super-)Poincaré generators. We also explain in detail the structure and charge-integrability of asymptotic symmetries with symmetry parameters depending on the fields (through the charges themselves), a topic relevant for nonlinear asymptotic symmetry algebras.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Fuentealba, M. Henneaux and C. Troessaert, Logarithmic supertranslations and supertranslation-invariant Lorentz charges, JHEP 02 (2023) 248 [arXiv:2211.10941] [INSPIRE].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
O. Fuentealba, M. Henneaux, S. Majumdar, J. Matulich and C. Troessaert, Asymptotic structure of the Pauli-Fierz theory in four spacetime dimensions, Class. Quant. Grav. 37 (2020) 235011 [arXiv:2007.12721] [INSPIRE].
R. Benguria, P. Cordero and C. Teitelboim, Aspects of the Hamiltonian Dynamics of Interacting Gravitational Gauge and Higgs Fields with Applications to Spherical Symmetry, Nucl. Phys. B 122 (1977) 61 [INSPIRE].
S.R. Coleman and J. Mandula, All Possible Symmetries of the S Matrix, Phys. Rev. 159 (1967) 1251 [INSPIRE].
O. Fuentealba, M. Henneaux and C. Troessaert, Asymptotic Symmetry Algebra of Einstein Gravity and Lorentz Generators, Phys. Rev. Lett. 131 (2023) 111402 [arXiv:2305.05436] [INSPIRE].
M. Mirbabayi and M. Porrati, Dressed Hard States and Black Hole Soft Hair, Phys. Rev. Lett. 117 (2016) 211301 [arXiv:1607.03120] [INSPIRE].
R. Bousso and M. Porrati, Soft Hair as a Soft Wig, Class. Quant. Grav. 34 (2017) 204001 [arXiv:1706.00436] [INSPIRE].
R. Javadinezhad, U. Kol and M. Porrati, Comments on Lorentz Transformations, Dressed Asymptotic States and Hawking Radiation, JHEP 01 (2019) 089 [arXiv:1808.02987] [INSPIRE].
R. Javadinezhad, U. Kol and M. Porrati, Supertranslation-invariant dressed Lorentz charges, JHEP 04 (2022) 069 [arXiv:2202.03442] [INSPIRE].
P.-N. Chen, M.-T. Wang, Y.-K. Wang and S.-T. Yau, Supertranslation invariance of angular momentum, Adv. Theor. Math. Phys. 25 (2021) 777 [arXiv:2102.03235] [INSPIRE].
P.-N. Chen, J. Keller, M.-T. Wang, Y.-K. Wang and S.-T. Yau, Evolution of Angular Momentum and Center of Mass at Null Infinity, Commun. Math. Phys. 386 (2021) 551 [arXiv:2102.03221] [INSPIRE].
G. Compère and D.A. Nichols, Classical and Quantized General-Relativistic Angular Momentum, arXiv:2103.17103 [INSPIRE].
G. Compère, S.E. Gralla and H. Wei, An asymptotic framework for gravitational scattering, Class. Quant. Grav. 40 (2023) 205018 [arXiv:2303.17124] [INSPIRE].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
O. Fuentealba, M. Henneaux, J. Matulich and C. Troessaert, Bondi-Metzner-Sachs Group in Five Spacetime Dimensions, Phys. Rev. Lett. 128 (2022) 051103 [arXiv:2111.09664] [INSPIRE].
O. Fuentealba, M. Henneaux, J. Matulich and C. Troessaert, Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis, JHEP 07 (2022) 149 [arXiv:2206.04972] [INSPIRE].
O. Fuentealba, M. Henneaux, S. Majumdar, J. Matulich and T. Neogi, Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations, Phys. Rev. D 104 (2021) L121702 [arXiv:2108.07825] [INSPIRE].
M. Henneaux and C. Troessaert, Asymptotic symmetries of electromagnetism at spatial infinity, JHEP 05 (2018) 137 [arXiv:1803.10194] [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, Princeton, U.S.A. (1992).
J. de Boer, F. Harmsze and T. Tjin, Nonlinear finite W symmetries and applications in elementary systems, Phys. Rept. 272 (1996) 139 [hep-th/9503161] [INSPIRE].
M. Henneaux, L. Maoz and A. Schwimmer, Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity, Annals Phys. 282 (2000) 31 [hep-th/9910013] [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
H. Afshar, A. Bagchi, R. Fareghbal, D. Grumiller and J. Rosseel, Spin-3 Gravity in Three-Dimensional Flat Space, Phys. Rev. Lett. 111 (2013) 121603 [arXiv:1307.4768] [INSPIRE].
H.A. Gonzalez, J. Matulich, M. Pino and R. Troncoso, Asymptotically flat spacetimes in three-dimensional higher spin gravity, JHEP 09 (2013) 016 [arXiv:1307.5651] [INSPIRE].
M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Hypersymmetry bounds and three-dimensional higher-spin black holes, JHEP 08 (2015) 021 [arXiv:1506.01847] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotically flat structure of hypergravity in three spacetime dimensions, JHEP 10 (2015) 009 [arXiv:1508.04663] [INSPIRE].
M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Extended anti-de Sitter Hypergravity in 2 + 1 Dimensions and Hypersymmetry Bounds, in International Workshop on Higher Spin Gauge Theories, Singapore (2015), pg. 139, https://doi.org/10.1142/9789813144101_0009 [arXiv:1512.08603] [INSPIRE].
O. Fuentealba, H.A. González, A. Pérez, D. Tempo and R. Troncoso, Superconformal Bondi-Metzner-Sachs Algebra in Three Dimensions, Phys. Rev. Lett. 126 (2021) 091602 [arXiv:2011.08197] [INSPIRE].
T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
H. Adami, D. Grumiller, M.M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo and C. Zwikel, Null boundary phase space: slicings, news & memory, JHEP 11 (2021) 155 [arXiv:2110.04218] [INSPIRE].
O. Fuentealba, M. Henneaux, S. Majumdar, J. Matulich and T. Neogi, Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity, JHEP 02 (2021) 031 [arXiv:2011.04669] [INSPIRE].
Acknowledgments
We thank Cédric Troessaert for important discussions. O.F. is grateful to the Collège de France for kind hospitality while this work was completed. This work was partially supported by a Marina Solvay Fellowship (O.F.) and by FNRS-Belgium (conventions FRFC PDRT.1025.14 and IISN 4.4503.15), as well as by funds from the Solvay Family.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2309.07600
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Fuentealba, O., Henneaux, M. Simplifying (super-)BMS algebras. J. High Energ. Phys. 2023, 108 (2023). https://doi.org/10.1007/JHEP11(2023)108
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2023)108