Abstract
Recently it was conjectured that a certain infinite-dimensional “diagonal” subgroup of BMS supertranslations acting on past and future null infinity ( and ) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg’s soft graviton theorem. Along the way we construct the canonical generators of supertranslations at , including the relevant soft graviton contributions. Boundary conditions at the past and future of and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
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References
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.
S. Weinberg, The quantum theory of fields. Volume 1: foundations, Cambridge University Press, Cambridge U.K. (1995).
A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [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].
A. Strominger, Asymptotic symmetries of Yang-Mills theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
J. Maldacena and A. Zhiboedov, Notes on soft factors, unpublished (2012).
J. Maldacena and A. Zhiboedov, private communication.
D. Christodoulou and S. Klainerman, The global nonlinear stability of the Minkowski space, Princeton University Press, Princeton U.S.A. (1993).
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, Supertranslations call for superrotations, PoS 21 (2010) 010 [arXiv:1102.4632] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
G. Barnich and C. Troessaert, Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity, JHEP 11 (2013) 003 [arXiv:1309.0794] [INSPIRE].
T. Banks, A critique of pure string theory: heterodox opinions of diverse dimensions, hep-th/0306074 [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].
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, Asymptotic quantization: based on 1984 Naples lectures, Bibliopolis, Naples Italy (1987).
S.Y. Choi, J.S. Shim and H.S. Song, Factorization and polarization in linearized gravity, Phys. Rev. D 51 (1995) 6 [hep-th/9411092] [INSPIRE].
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ArXiv ePrint: 1401.7026
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He, T., Lysov, V., Mitra, P. et al. BMS supertranslations and Weinberg’s soft graviton theorem. J. High Energ. Phys. 2015, 151 (2015). https://doi.org/10.1007/JHEP05(2015)151
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DOI: https://doi.org/10.1007/JHEP05(2015)151