Abstract
We present strong evidence that the sub-subleading soft theorem in semiclassical (tree level) gravity discovered by Cachazo and Strominger is equivalent to the conservation of asymptotic charges associated to a new class of vector fields not contained within the previous extensions of BMS algebra. Our analysis crucially relies on analyzing the hitherto established equivalences between soft theorems and Ward identities from a new perspective. In this process we naturally (re)discover a class of ‘magnetic’ charges at null infinity that are associated to the dual of the Weyl tensor.
Article PDF
Similar content being viewed by others
References
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].
A. Ashtekar, Asymptotic quantization of the gravitational field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
A. Ashtekar and M. Streubel, Symplectic geometry of radiative modes and conserved quantities at null infinity, Proc. Roy. Soc. Lond. A 376 (1981) 585 [INSPIRE].
A. Ashtekar, Radiative degrees of freedom of the gravitational field in exact general relativity, J. Math. Phys. 22 (1981) 2885 [INSPIRE].
A. Ashtekar, Asymptotic quantization, Bibliopolis, Naples, Italy (1987).
A. Ashtekar and A. Sen, NUT 4-momenta are forever, J. Math. Phys. 23 (1982) 2168.
A. Ashtekar, Geometry and physics of null infinity, arXiv:1409.1800 [INSPIRE].
A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.
F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [INSPIRE].
J. Broedel, M. de Leeuw, J. Plefka and M. Rosso, Constraining subleading soft gluon and graviton theorems, Phys. Rev. D 90 (2014) 065024 [arXiv:1406.6574] [INSPIRE].
Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-energy behavior of gluons and gravitons from gauge invariance, Phys. Rev. D 90 (2014) 084035 [arXiv:1406.6987] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity \( \mathcal{S} \) -matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
M. Campiglia and A. Laddha, New symmetries for the gravitational S-matrix, JHEP 04 (2015) 076 [arXiv:1502.02318] [INSPIRE].
S. He, Y.-t. Huang and C. Wen, Loop corrections to soft theorems in gauge theories and gravity, JHEP 12 (2014) 115 [arXiv:1405.1410] [INSPIRE].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [INSPIRE].
M. Campiglia and A. Laddha, Sub-subleading soft gravitons: new symmetries of quantum gravity?, Phys. Lett. B 764 (2017) 218 [arXiv:1605.09094] [INSPIRE].
S.G. Avery and B.U.W. Schwab, Burg-Metzner-Sachs symmetry, string theory and soft theorems, Phys. Rev. D 93 (2016) 026003 [arXiv:1506.05789] [INSPIRE].
A. Ashtekar, L. Bombelli and O. Reula. The covariant phase space of asymptotically flat gravitational fields, in Analysis, Geometry and Mechanics: 200 Years After Lagrange, M. Francaviglia ed., North-Holland, The Netherlands (1991).
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP 12 (2015) 094 [arXiv:1509.01406] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
V. Lysov, S. Pasterski and A. Strominger, Low-subleading soft theorem as a symmetry of QED, Phys. Rev. Lett. 113 (2014) 111601 [arXiv:1407.3814] [INSPIRE].
J. Jezierski and M. Lukasik, Conformal Yano-Killing tensor for the Kerr metric and conserved quantities, Class. Quant. Grav. 23 (2006) 2895 [gr-qc/0510058] [INSPIRE].
A. Ashtekar and R.O. Hansen, A unified treatment of null and spatial infinity in general relativity. I — Universal structure, asymptotic symmetries and conserved quantities at spatial infinity, J. Math. Phys. 19 (1978) 1542 [INSPIRE].
G. Compere, F. Dehouck and A. Virmani, On asymptotic flatness and Lorentz charges, Class. Quant. Grav. 28 (2011) 145007 [arXiv:1103.4078] [INSPIRE].
R.M. Wald, General relativity, Chicago University Press, Chicago, U.S.A. (1984).
R. Penrose and W. Rindler, Spinors and space-time. Volume 2: spinor and twistor methods in space-time geometry, Cambridge University Press, Cambridge, U.K. (1988).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1608.00685
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Campiglia, M., Laddha, A. Sub-subleading soft gravitons and large diffeomorphisms. J. High Energ. Phys. 2017, 36 (2017). https://doi.org/10.1007/JHEP01(2017)036
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2017)036