External sources; Field theory; Gravitational radiation; Kinematics properties; Spacetime; Ward identities; Physics and Astronomy (all); High Energy Physics - Theory; General Relativity and Quantum Cosmology; General Physics and Astronomy
Abstract :
[en] We show that a 3D sourced conformal Carrollian field theory has the right kinematic properties to holographically describe gravity in 4D asymptotically flat spacetime. The external sources encode the leaks of gravitational radiation at null infinity. The Ward identities of this theory are shown to reproduce those of the 2D celestial CFT after relating Carrollian to celestial operators. This suggests a new set of interplays between gravity in asymptotically flat spacetime, sourced conformal Carrollian field theory and celestial CFT.
Research center :
AGIF - Algèbre, Géométrie et Interactions fondamentales
Disciplines :
Physics
Author, co-author :
Donnay, Laura ; Institute for Theoretical Physics, TU Wien Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria
Fiorucci, Adrien ; Institute for Theoretical Physics, TU Wien Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria
S827 - Physique de l'Univers, Champs et Gravitation
Research institute :
Complexys
European Projects :
H2020 - 101002551 - HiSS - Higher Spin Symmetry in Quantum Gravity, Condensed Matter and Mathematics
Funders :
Austrian Science Fund H2020 European Research Council Erwin Schrödinger International Institute for Mathematics and Physics Union Européenne
Funding number :
101002551
Funding text :
We would like to thank Glenn Barnich, Geoffrey Compère, Florian Ecker, Gaston Giribet, Daniel Grumiller, and Marios Petropoulos for discussions. L. D., A. F., and R. R. are supported by the Austrian Science Fund (FWF) START project Y 1447-N. A. F. and R. R. also acknowledge support from the FWF, project P 32581-N. Y. H. has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 101002551). The authors also acknowledge support of the Erwin Schrödinger Institute (ESI) in Vienna where part of this work was conducted during the thematic program “Geometry for Higher Spin Gravity_FCC_2021”.
G. 't Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308, 284 (1993).
L. Susskind, The world as a hologram, J. Math. Phys. (N.Y.) 36, 6377 (1995). JMAPAQ 0022-2488 10.1063/1.531249
J. M. Maldacena, The large (Equation presented) limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998). 1095-0761 10.4310/ATMP.1998.v2.n2.a1
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998). 1095-0761 10.4310/ATMP.1998.v2.n2.a2
O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large (Equation presented) field theories, string theory and gravity, Phys. Rep. 323, 183 (2000). PRPLCM 0370-1573 10.1016/S0370-1573(99)00083-6
L. Susskind, Holography in the flat space limit, AIP Conf. Proc. 493, 98 (1999). APCPCS 0094-243X 10.1063/1.1301570
J. Polchinski, S matrices from AdS space-time, arXiv:hep-th/9901076.
S. B. Giddings, Flat space scattering and bulk locality in the (Equation presented) correspondence, Phys. Rev. D 61, 106008 (2000). PRVDAQ 0556-2821 10.1103/PhysRevD.61.106008
J. de Boer and S. N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B665, 545 (2003). NUPBBO 0550-3213 10.1016/S0550-3213(03)00494-2
G. Arcioni and C. Dappiaggi, Holography in asymptotically flat space-times and the BMS group, Classical Quantum Gravity 21, 5655 (2004). CQGRDG 0264-9381 10.1088/0264-9381/21/23/022
G. Arcioni and C. Dappiaggi, Exploring the holographic principle in asymptotically flat space-times via the BMS group, Nucl. Phys. B674, 553 (2003). NUPBBO 0550-3213 10.1016/j.nuclphysb.2003.09.051
R. B. Mann and D. Marolf, Holographic renormalization of asymptotically flat spacetimes, Classical Quantum Gravity 23, 2927 (2006). CQGRDG 0264-9381 10.1088/0264-9381/23/9/010
H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. VII. Waves from axisymmetric isolated systems, Proc. R. Soc. A 269, 21 (1962). PRLAAZ 1364-5021 10.1098/rspa.1962.0161
R. K. Sachs, Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-times, Proc. R. Soc. A 270, 103 (1962). PRLAAZ 1364-5021 10.1098/rspa.1962.0206
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962). PHRVAO 0031-899X 10.1103/PhysRev.128.2851
C. Dappiaggi, BMS field theory and holography in asymptotically flat space-times, J. High Energy Phys. 11 (2004) 011. JHEPFG 1029-8479 10.1088/1126-6708/2004/11/011
C. Dappiaggi, V. Moretti, and N. Pinamonti, Rigorous steps towards holography in asymptotically flat spacetimes, Rev. Math. Phys. 18, 349 (2006). RMPHEX 0129-055X 10.1142/S0129055X0600270X
A. Bagchi, R. Basu, A. Kakkar, and A. Mehra, Flat holography: Aspects of the dual field theory, J. High Energy Phys. 12 (2016) 147. JHEPFG 1029-8479 10.1007/JHEP12(2016)147
A. Bagchi, A. Mehra, and P. Nandi, Field theories with conformal Carrollian symmetry, J. High Energy Phys. 05 (2019) 108. JHEPFG 1029-8479 10.1007/JHEP05(2019)108
A. Bagchi, R. Basu, A. Mehra, and P. Nandi, Field theories on null manifolds, J. High Energy Phys. 02 (2020) 141. JHEPFG 1029-8479 10.1007/JHEP02(2020)141
A. Laddha, S. G. Prabhu, S. Raju, and P. Shrivastava, The holographic nature of null infinity, SciPost Phys. 10, 041 (2021). SPCHCW 2542-4653 10.21468/SciPostPhys.10.2.041
B. Chen, R. Liu, and Y.-f. Zheng, On higher-dimensional Carrollian and Galilean conformal field theories, arXiv:2112.10514.
A. Bagchi, D. Grumiller, and P. Nandi, Carrollian superconformal theories and super BMS, J. High Energy Phys. 05 (2022) 044. JHEPFG 1029-8479 10.1007/JHEP05(2022)044
C. Duval, G. W. Gibbons, and P. A. Horvathy, Conformal Carroll groups and BMS symmetry, Classical Quantum Gravity 31, 092001 (2014). CQGRDG 0264-9381 10.1088/0264-9381/31/9/092001
C. Duval, G. W. Gibbons, and P. A. Horvathy, Conformal Carroll groups, J. Phys. A 47, 335204 (2014). JPAMB5 1751-8113 10.1088/1751-8113/47/33/335204
G. Barnich, A. Gomberoff, and H. A. Gonzalez, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86, 024020 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.86.024020
G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, J. High Energy Phys. 10 (2012) 095. JHEPFG 1029-8479 10.1007/JHEP10(2012)095
A. Bagchi, S. Detournay, R. Fareghbal, and J. Simón, Holography of 3D Flat Cosmological Horizons, Phys. Rev. Lett. 110, 141302 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.141302
A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards flatspace holography from non-relativistic symmetries, J. High Energy Phys. 10 (2012) 092. JHEPFG 1029-8479 10.1007/JHEP10(2012)092
S. Detournay, D. Grumiller, F. Schöller, and J. Simón, Variational principle and one-point functions in three-dimensional flat space Einstein gravity, Phys. Rev. D 89, 084061 (2014). PRVDAQ 1550-7998 10.1103/PhysRevD.89.084061
A. Bagchi, R. Basu, D. Grumiller, and M. Riegler, Entanglement Entropy in Galilean Conformal Field Theories and Flat Holography, Phys. Rev. Lett. 114, 111602 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.111602
A. Bagchi, D. Grumiller, and W. Merbis, Stress tensor correlators in three-dimensional gravity, Phys. Rev. D 93, 061502(R) (2016). PRVDAQ 2470-0010 10.1103/PhysRevD.93.061502
J. Hartong, Holographic reconstruction of 3D flat space-time, J. High Energy Phys. 10 (2016) 104. JHEPFG 1029-8479 10.1007/JHEP10(2016)104
S. Bhattacharyya, V. E. Hubeny, S. Minwalla, and M. Rangamani, Nonlinear fluid dynamics from gravity, J. High Energy Phys. 02 (2008) 045. JHEPFG 1029-8479 10.1088/1126-6708/2008/02/045
S. Bhattacharyya, R. Loganayagam, I. Mandal, S. Minwalla, and A. Sharma, Conformal nonlinear fluid dynamics from gravity in arbitrary dimensions, J. High Energy Phys. 12 (2008) 116. JHEPFG 1029-8479 10.1088/1126-6708/2008/12/116
R. F. Penna, (Equation presented) invariant fluid dynamics at null infinity, Classical Quantum Gravity 35, 044002 (2018). CQGRDG 0264-9381 10.1088/1361-6382/aaa3aa
L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids, Classical Quantum Gravity 35, 165001 (2018). CQGRDG 0264-9381 10.1088/1361-6382/aacf1a
L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, Flat holography and Carrollian fluids, J. High Energy Phys. 07 (2018) 165. JHEPFG 1029-8479 10.1007/JHEP07(2018)165
A. Campoleoni, L. Ciambelli, C. Marteau, P. M. Petropoulos, and K. Siampos, Two-dimensional fluids and their holographic duals, Nucl. Phys. B946, 114692 (2019). NUPBBO 0550-3213 10.1016/j.nuclphysb.2019.114692
L. Ciambelli, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Gauges in three-dimensional gravity and holographic fluids, J. High Energy Phys. 11 (2020) 092. JHEPFG 1029-8479 10.1007/JHEP11(2020)092
L. Ciambelli, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Fefferman-Graham and Bondi gauges in the fluid/gravity correspondence, Proc. Sci., CORFU2019 (2020) 154. 1824-8039 10.22323/1.376.0154
S. Pasterski, S.-H. Shao, and A. Strominger, Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96, 065026 (2017). PRVDAQ 2470-0010 10.1103/PhysRevD.96.065026
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96, 065022 (2017). PRVDAQ 2470-0010 10.1103/PhysRevD.96.065022
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press, Princeton, NJ, 2018).
L. Donnay, A. Puhm, and A. Strominger, Conformally soft photons and gravitons, J. High Energy Phys. 01 (2019) 184. JHEPFG 1029-8479 10.1007/JHEP01(2019)184
A. Fotopoulos and T. R. Taylor, Primary fields in celestial CFT, J. High Energy Phys. 10 (2019) 167. JHEPFG 1029-8479 10.1007/JHEP10(2019)167
M. Pate, A.-M. Raclariu, and A. Strominger, Conformally soft theorem in gauge theory, Phys. Rev. D 100, 085017 (2019). PRVDAQ 2470-0010 10.1103/PhysRevD.100.085017
W. Fan, A. Fotopoulos, and T. R. Taylor, Soft limits of Yang-Mills amplitudes and conformal correlators, J. High Energy Phys. 05 (2019) 121. JHEPFG 1029-8479 10.1007/JHEP05(2019)121
L. Donnay, S. Pasterski, and A. Puhm, Asymptotic symmetries and celestial CFT, J. High Energy Phys. 09 (2020) 176. JHEPFG 1029-8479 10.1007/JHEP09(2020)176
A. Guevara, E. Himwich, M. Pate, and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, J. High Energy Phys. 11 (2021) 152. JHEPFG 1029-8479 10.1007/JHEP11(2021)152
A. Strominger, (Equation presented) Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries, Phys. Rev. Lett. 127, 221601 (2021). PRLTAO 0031-9007 10.1103/PhysRevLett.127.221601
J. Mago, L. Ren, A. Y. Srikant, and A. Volovich, Deformed (Equation presented) algebras in the celestial CFT, arXiv:2111.11356.
S. Pasterski, M. Pate, and A.-M. Raclariu, Celestial holography, arXiv:2111.11392.
L. A. Tamburino and J. H. Winicour, Gravitational fields in finite and conformal Bondi frames, Phys. Rev. 150, 1039 (1966). PHRVAO 0031-899X 10.1103/PhysRev.150.1039
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, J. High Energy Phys. 05 (2010) 062. JHEPFG 1029-8479 10.1007/JHEP05(2010)062
A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152. JHEPFG 1029-8479 10.1007/JHEP07(2014)152
T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg's soft graviton theorem, J. High Energy Phys. 05 (2015) 151. JHEPFG 1029-8479 10.1007/JHEP05(2015)151
R. Geroch, Asymptotic structure of space-time, in Asymptotic Structure of Space-Time, edited by F. P. Esposito and L. Witten (Springer, Boston, MA, 1977).
M. Henneaux, Geometry of zero signature space-times, Bull. Soc. Math. Belg. 31, 47 (1979).
A. Ashtekar, Geometry and physics of null infinity, arXiv:1409.1800.
L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, Carroll structures, null geometry and conformal isometries, Phys. Rev. D 100, 046010 (2019). PRVDAQ 2470-0010 10.1103/PhysRevD.100.046010
J. Figueroa-O'Farrill, R. Grassie, and S. Prohazka, Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes, J. High Energy Phys. 08 (2019) 119. JHEPFG 1029-8479 10.1007/JHEP08(2019)119
Y. Herfray, Asymptotic shear and the intrinsic conformal geometry of null-infinity, J. Math. Phys. (N.Y.) 61, 072502 (2020). JMAPAQ 0022-2488 10.1063/5.0003616
Y. Herfray, Tractor geometry of asymptotically flat space-times, Ann. Henri Poincaré (2022) 10.1007/s00023-022-01174-0.
Y. Herfray, Carrollian manifolds and null infinity: A view from Cartan geometry, arXiv:2112.09048.
M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, J. High Energy Phys. 11 (2021) 180. JHEPFG 1029-8479 10.1007/JHEP11(2021)180
D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity (Equation presented)-matrix, J. High Energy Phys. 08 (2014) 058. JHEPFG 1029-8479 10.1007/JHEP08(2014)058
S. W. Hawking, M. J. Perry, and A. Strominger, Superrotation charge and supertranslation hair on black holes, J. High Energy Phys. 05 (2017) 161. JHEPFG 1029-8479 10.1007/JHEP05(2017)161
G. Compère, A. Fiorucci, and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, J. High Energy Phys. 11 (2018) 200. JHEPFG 1029-8479 10.1007/JHEP11(2018)200
M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101, 104039 (2020). PRVDAQ 2470-0010 10.1103/PhysRevD.101.104039
G. Compère, A. Fiorucci, and R. Ruzziconi, The (Equation presented) charge algebra, J. High Energy Phys. 10 (2020) 205. JHEPFG 1029-8479 10.1007/JHEP10(2020)205
A. Fiorucci, Leaky covariant phase spaces: Theory and application to (Equation presented)-BMS symmetry, Ph.D. thesis, Brussels University, International Solvay Institutes, Brussels, 2021, arXiv:2112.07666.
L. Donnay and R. Ruzziconi, BMS flux algebra in celestial holography, J. High Energy Phys. 11 (2021) 040. JHEPFG 1029-8479 10.1007/JHEP11(2021)040
T. Dray and M. Streubel, Angular momentum at null infinity, Classical Quantum Gravity 1, 15 (1984). CQGRDG 0264-9381 10.1088/0264-9381/1/1/005
R. M. Wald and A. Zoupas, A general definition of 'conserved quantities' in general relativity and other theories of gravity, Phys. Rev. D 61, 084027 (2000). PRVDAQ 0556-2821 10.1103/PhysRevD.61.084027
G. Barnich and C. Troessaert, BMS charge algebra, J. High Energy Phys. 12 (2011) 105. JHEPFG 1029-8479 10.1007/JHEP12(2011)105
E. E. Flanagan and D. A. Nichols, Conserved charges of the extended Bondi-Metzner-Sachs algebra, Phys. Rev. D 95, 044002 (2017). PRVDAQ 2470-0010 10.1103/PhysRevD.95.044002
G. Compère, R. Oliveri, and A. Seraj, The Poincaré and BMS flux-balance laws with application to binary systems, J. High Energy Phys. 10 (2020) 116. JHEPFG 1029-8479 10.1007/JHEP10(2020)116
C. Troessaert, Hamiltonian surface charges using external sources, J. Math. Phys. (N.Y.) 57, 053507 (2016). JMAPAQ 0022-2488 10.1063/1.4947177
L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, The Weyl BMS group and Einstein's equations, J. High Energy Phys. 07 (2021) 170. JHEPFG 1029-8479 10.1007/JHEP07(2021)170
L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, Extended corner symmetry, charge bracket and Einstein's equations, J. High Energy Phys. 09 (2021) 083. JHEPFG 1029-8479 10.1007/JHEP09(2021)083
W. Wieland, Barnich-Troessaert bracket as a Dirac bracket on the covariant phase space, Classical Quantum Gravity 39, 025016 (2022). CQGRDG 0264-9381 10.1088/1361-6382/ac3e52
L. Freidel, A canonical bracket for open gravitational system, arXiv:2111.14747.
V. Chandrasekaran, E. E. Flanagan, I. Shehzad, and A. J. Speranza, A general framework for gravitational charges and holographic renormalization, Int. J. Mod. Phys. A 10.1142/S0217751X22501056.
W. Wieland, Null infinity as an open Hamiltonian system, J. High Energy Phys. 04 (2021) 095. JHEPFG 1029-8479 10.1007/JHEP04(2021)095
G. Barnich, A. Fiorucci, and R. Ruzziconi (to be published).
See, e.g., Ref. [88] for the standard derivation of Ward identities. The consideration of external sources in this derivation will be detailed in an upcoming work.
P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics (Springer-Verlag, New York, 1997).
J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Perfect fluids, SciPost Phys. 5, 003 (2018). SPCHCW 2542-4653 10.21468/SciPostPhys.5.1.003
L. Ciambelli and C. Marteau, Carrollian conservation laws and Ricci-flat gravity, Classical Quantum Gravity 36, 085004 (2019). CQGRDG 0264-9381 10.1088/1361-6382/ab0d37
L. Donnay and C. Marteau, Carrollian physics at the Black Hole Horizon, Classical Quantum Gravity 36, 165002 (2019). CQGRDG 0264-9381 10.1088/1361-6382/ab2fd5
J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll symmetry, dark energy and inflation, Front. Phys. 10, 810405 (2022). 10.3389/fphy.2022.810405
V. Chandrasekaran, E. E. Flanagan, I. Shehzad, and A. J. Speranza, Brown-York charges at null boundaries, J. High Energy Phys. 01 (2022) 02. JHEPFG 1029-8479 10.1007/JHEP01(2022)029
L. Freidel and D. Pranzetti, Gravity from symmetry: Duality and impulsive waves, J. High Energy Phys. 04 (2022) 125. JHEPFG 1029-8479 10.1007/JHEP04(2022)125
L. Freidel, D. Pranzetti, and A.-M. Raclariu, Sub-subleading soft graviton theorem from asymptotic Einstein's equations, J. High Energy Phys. 05 (2022) 186. JHEPFG 1029-8479 10.1007/JHEP05(2022)186
J. Isberg, U. Lindstrom, B. Sundborg, and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys. B411, 122 (1994). NUPBBO 0550-3213 10.1016/0550-3213(94)90056-6
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, J. High Energy Phys. 07 (2014) 048. JHEPFG 1029-8479 10.1007/JHEP07(2014)048
A. Bagchi, S. Chakrabortty, and P. Parekh, Tensionless strings from worldsheet symmetries, J. High Energy Phys. 01 (2016) 158. JHEPFG 1029-8479 10.1007/JHEP01(2016)158
P.-x. Hao, W. Song, X. Xie, and Y. Zhong, A BMS-invariant free scalar model, Phys. Rev. D 105, 125005 (2022). PRVDAQ 2470-0010 10.1103/PhysRevD.105.125005
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208, 413 (1999). CMPHAY 0010-3616 10.1007/s002200050764
S. de Haro, S. N. Solodukhin, and K. Skenderis, Holographic reconstruction of space-time and renormalization in the (Equation presented) correspondence, Commun. Math. Phys. 217, 595 (2001). CMPHAY 0010-3616 10.1007/s002200100381
C. Troessaert, The BMS4 algebra at spatial infinity, Classical Quantum Gravity 35, 074003 (2018). CQGRDG 0264-9381 10.1088/1361-6382/aaae22
G. Compère and A. Fiorucci, Asymptotically flat spacetimes with (Equation presented) symmetry, Classical Quantum Gravity 34, 204002 (2017). CQGRDG 0264-9381 10.1088/1361-6382/aa8aad
M. Henneaux and C. Troessaert, BMS group at spatial infinity: the Hamiltonian (ADM) approach, J. High Energy Phys. 03 (2018) 147. JHEPFG 1029-8479 10.1007/JHEP03(2018)147
M. Henneaux and C. Troessaert, Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity, J. High Energy Phys. 07 (2018) 171. JHEPFG 1029-8479 10.1007/JHEP07(2018)171
K. Prabhu, Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity, J. High Energy Phys. 03 (2019) 148. JHEPFG 1029-8479 10.1007/JHEP03(2019)148
K. Prabhu and I. Shehzad, Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity, arXiv:2110.04900.
A. Bagchi and I. Mandal, On representations and correlation functions of Galilean conformal algebras, Phys. Lett. B 675, 393 (2009). PYLBAJ 0370-2693 10.1016/j.physletb.2009.04.030
A. Bagchi, M. Gary, and Zodinmawia, The nuts and bolts of the BMS bootstrap, Classical Quantum Gravity 34, 174002 (2017). CQGRDG 0264-9381 10.1088/1361-6382/aa8003
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46, 573 (1981). PRLTAO 0031-9007 10.1103/PhysRevLett.46.573
A. Ashtekar and M. Streubel, Symplectic geometry of radiative modes and conserved quantities at null infinity, Proc. R. Soc. A 376, 585 (1981). PRLAAZ 1364-5021 10.1098/rspa.1981.0109
D. Kapec, P. Mitra, A.-M. Raclariu, and A. Strominger, 2D Stress Tensor for 4D Gravity, Phys. Rev. Lett. 119, 121601 (2017). PRLTAO 0031-9007 10.1103/PhysRevLett.119.121601
C. Cheung, A. de la Fuente, and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, J. High Energy Phys. 01 (2017) 112. JHEPFG 1029-8479 10.1007/JHEP01(2017)112
A. Fotopoulos, S. Stieberger, T. R. Taylor, and B. Zhu, Extended BMS algebra of celestial CFT, J. High Energy Phys. 03 (2020) 130. JHEPFG 1029-8479 10.1007/JHEP03(2020)130
G. Compère, A. Fiorucci, and R. Ruzziconi, The (Equation presented) group of (Equation presented) and new boundary conditions for (Equation presented), Classical Quantum Gravity 36, 195017 (2019); CQGRDG 0264-9381 10.1088/1361-6382/ab3d4b
G. Compère, A. Fiorucci, and R. Ruzziconi Classical Quantum Gravity 38, 229501(E) (2021). CQGRDG 0264-9381 10.1088/1361-6382/ac2c1a
A. Fiorucci and R. Ruzziconi, Charge algebra in (Equation presented) spacetimes, J. High Energy Phys. 05 (2021) 210. JHEPFG 1029-8479 10.1007/JHEP05(2021)210
