Abstract
Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from “magnetic” and “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.
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References
J.-M. Lévy-Leblond, Une nouvelle limite non-relativiste du groupe de Poincaré (in French), Ann. I.H.P. Phys. Théor. 3 (1965) 1.
H. Bacry and J. Levy-Leblond, Possible kinematics, J. Math. Phys. 9 (1968) 1605 [INSPIRE].
G. Daŭtcourt, Characteristic hypersurfaces in general relativity. I, J. Math. Phys. 8 (1967) 1492.
R. Fareghbal and A. Naseh, Flat-space energy-momentum tensor from BMS/GCA correspondence, JHEP 03 (2014) 005 [arXiv:1312.2109] [INSPIRE].
G. Dautcourt, On the ultrarelativistic limit of general relativity, Acta Phys. Polon. B 29 (1998) 1047 [gr-qc/9801093] [INSPIRE].
C. Duval, G.W. Gibbons, P.A. Horvathy and P.M. Zhang, Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time, Class. Quant. Grav. 31 (2014) 085016 [arXiv:1402.0657] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
E. Bergshoeff, J. Gomis and G. Longhi, Dynamics of Carroll particles, Class. Quant. Grav. 31 (2014) 205009 [arXiv:1405.2264] [INSPIRE].
R. Fareghbal and A. Naseh, Aspects of flat/CCFT correspondence, Class. Quant. Grav. 32 (2015) 135013 [arXiv:1408.6932] [INSPIRE].
B. Cardona, J. Gomis and J.M. Pons, Dynamics of Carroll strings, JHEP 07 (2016) 050 [arXiv:1605.05483] [INSPIRE].
E. Bergshoeff, D. Grumiller, S. Prohazka and J. Rosseel, Three-dimensional spin-3 theories based on general kinematical algebras, JHEP 01 (2017) 114 [arXiv:1612.02277] [INSPIRE].
C. Duval, G.W. Gibbons, P.A. Horvathy and P.M. Zhang, Carroll symmetry of plane gravitational waves, Class. Quant. Grav. 34 (2017) 175003 [arXiv:1702.08284] [INSPIRE].
D. Grumiller, W. Merbis and M. Riegler, Most general flat space boundary conditions in three-dimensional Einstein gravity, Class. Quant. Grav. 34 (2017) 184001 [arXiv:1704.07419] [INSPIRE].
L. Ciambelli, C. Marteau, A.C. Petkou, P.M. Petropoulos and K. Siampos, Flat holography and Carrollian fluids, JHEP 07 (2018) 165 [arXiv:1802.06809] [INSPIRE].
J. Figueroa-O’Farrill and S. Prohazka, Spatially isotropic homogeneous spacetimes, JHEP 01 (2019) 229 [arXiv:1809.01224] [INSPIRE].
A. Barducci, R. Casalbuoni and J. Gomis, Vector SUSY models with Carroll or Galilei invariance, Phys. Rev. D 99 (2019) 045016 [arXiv:1811.12672] [INSPIRE].
K. Morand, Embedding Galilean and Carrollian geometries I. Gravitational waves, J. Math. Phys. 61 (2020) 082502 [arXiv:1811.12681] [INSPIRE].
R.F. Penna, Near-horizon Carroll symmetry and black hole Love numbers, arXiv:1812.05643 [INSPIRE].
A. Bagchi, A. Mehra and P. Nandi, Field theories with conformal Carrollian symmetry, JHEP 05 (2019) 108 [arXiv:1901.10147] [INSPIRE].
L. Donnay and C. Marteau, Carrollian physics at the black hole horizon, Class. Quant. Grav. 36 (2019) 165002 [arXiv:1903.09654] [INSPIRE].
J. Figueroa-O’Farrill, R. Grassie and S. Prohazka, Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes, JHEP 08 (2019) 119 [arXiv:1905.00034] [INSPIRE].
L. Ravera, AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit, Phys. Lett. B 795 (2019) 331 [arXiv:1905.00766] [INSPIRE].
L. Ciambelli, R.G. Leigh, C. Marteau and P.M. Petropoulos, Carroll structures, null geometry and conformal isometries, Phys. Rev. D 100 (2019) 046010 [arXiv:1905.02221] [INSPIRE].
J. Gomis, A. Kleinschmidt, J. Palmkvist and P. Salgado-Rebolledó, Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity, JHEP 02 (2020) 009 [arXiv:1912.07564] [INSPIRE].
A. Bagchi, R. Basu, A. Mehra and P. Nandi, Field theories on null manifolds, JHEP 02 (2020) 141 [arXiv:1912.09388] [INSPIRE].
K. Banerjee, R. Basu, A. Mehra, A. Mohan and A. Sharma, Interacting conformal Carrollian theories: cues from electrodynamics, Phys. Rev. D 103 (2021) 105001 [arXiv:2008.02829] [INSPIRE].
D. Grumiller, J. Hartong, S. Prohazka and J. Salzer, Limits of JT gravity, JHEP 02 (2021) 134 [arXiv:2011.13870] [INSPIRE].
J. Gomis, D. Hidalgo and P. Salgado-Rebolledó, Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity, JHEP 05 (2021) 162 [arXiv:2011.15053] [INSPIRE].
A. Bagchi, S. Chakrabortty, D. Grumiller, B. Radhakrishnan, M. Riegler and A. Sinha, Non-Lorentzian chaos and cosmological holography, Phys. Rev. D 104 (2021) L101901 [arXiv:2106.07649] [INSPIRE].
P. Concha, D. Peñafiel, L. Ravera and E. Rodríguez, Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant, Phys. Lett. B 823 (2021) 136735 [arXiv:2107.05716] [INSPIRE].
R. Casalbuoni, J. Gomis and D. Hidalgo, World-line description of fractons, arXiv:2107.09010 [INSPIRE].
F. Peña-Benitez, Fractons, symmetric gauge fields and geometry, arXiv:2107.13884 [INSPIRE].
S. Azarnia, R. Fareghbal, A. Naseh and H. Zolfi, Islands in flat-space cosmology, arXiv:2109.04795 [INSPIRE].
A. Campoleoni and S. Pekar, Carrollian and Galilean conformal higher-spin algebras in any dimensions, arXiv:2110.07794 [INSPIRE].
L. Marsot, Planar Carrollean dynamics, and the Carroll quantum equation, arXiv:2110.08489 [INSPIRE].
M. Henneaux and P. Salgado-Rebolledó, Carroll contractions of Lorentz-invariant theories, JHEP 11 (2021) 180 [arXiv:2109.06708] [INSPIRE].
J. de Boer, J. Hartong, N.A. Obers, W. Sybesma and S. Vandoren, Carroll symmetry, dark energy and inflation, arXiv:2110.02319 [INSPIRE].
C.J. Isham, Some quantum field theory aspects of the superspace quantization of general relativity, Proc. Roy. Soc. Lond. A 351 (1976) 209 [INSPIRE].
C. Teitelboim, Surface deformations, their square root and the signature of space-time, in 7th International group theory colloquium: the integrative conference on group theory and mathematical physics, (1978).
M. Henneaux, Geometry of zero signature space-times, Bull. Soc. Math. Belg. 31 (1979) 47.
C. Teitelboim, Quantum mechanics of the gravitational field, Phys. Rev. D 25 (1982) 3159 [INSPIRE].
M. Henneaux, M. Pilati and C. Teitelboim, Explicit solution for the zero signature (strong coupling) limit of the propagation amplitude in quantum gravity, Phys. Lett. B 110 (1982) 123 [INSPIRE].
C. Teitelboim, Quantum mechanics of the gravitational field in asymptotically flat space, Phys. Rev. D 28 (1983) 310 [INSPIRE].
V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz, Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys. 19 (1970) 525 [INSPIRE].
V.a. Belinsky, I.m. Khalatnikov and E.m. Lifshitz, A general solution of the Einstein equations with a time singularity, Adv. Phys. 31 (1982) 639 [INSPIRE].
M. Henneaux, Quantification hamiltonienne du champ de gravitation: une nouvelle approche (in French), Bull. Acad. Roy. Belgique 68 (1982) 940.
T. Damour, M. Henneaux and H. Nicolai, Cosmological billiards, Class. Quant. Grav. 20 (2003) R145 [hep-th/0212256] [INSPIRE].
J. Hartong, Gauging the Carroll algebra and ultra-relativistic gravity, JHEP 08 (2015) 069 [arXiv:1505.05011] [INSPIRE].
E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel and T. ter Veldhuis, Carroll versus Galilei gravity, JHEP 03 (2017) 165 [arXiv:1701.06156] [INSPIRE].
C. Teitelboim, How commutators of constraints reflect the space-time structure, Annals Phys. 79 (1973) 542 [INSPIRE].
C. Teitelboim, The Hamiltonian structure of space-time, Ph.D. thesis, unpublished, (1973).
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].
T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
M. Henneaux and C. Troessaert, BMS group at spatial infinity: the Hamiltonian (ADM) approach, JHEP 03 (2018) 147 [arXiv:1801.03718] [INSPIRE].
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. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
C. Bunster, A. Gomberoff and A. Pérez, Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces, in Tullio Regge: an eclectic genius, from quantum gravity to computer play, L. Castellani, A. Ceresola, R. D’Auria and P. Fré eds., World Scientific, Singapore (2019) [arXiv:1805.03728] [INSPIRE].
C. Bunster, A. Gomberoff and A. Pérez, Bondi-Metzner-Sachs invariance and electric-magnetic duality, Phys. Rev. D 101 (2020) 044003 [arXiv:1905.07514] [INSPIRE].
M. Henneaux and C. Troessaert, Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity, JHEP 07 (2018) 171 [arXiv:1805.11288] [INSPIRE].
M. Henneaux and C. Troessaert, The asymptotic structure of gravity at spatial infinity in four spacetime dimensions, arXiv:1904.04495 [INSPIRE].
A. Pérez, Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant, CECS-PHY-21/04, work in progress.
R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
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Pérez, A. Asymptotic symmetries in Carrollian theories of gravity. J. High Energ. Phys. 2021, 173 (2021). https://doi.org/10.1007/JHEP12(2021)173
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DOI: https://doi.org/10.1007/JHEP12(2021)173