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BMS supertranslations and Weinberg's soft graviton theorem · Around

2014

BMS supertranslations and Weinberg's soft graviton theorem

He, Temple, Lysov, Vyacheslav, Mitra, Prahar et al.

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Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity (${\mathscr I}^-$ and ${\mathscr I}^+$) is an exact symmetry of the quantum gravity ${\cal S}$-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 ${\mathscr I}^\pm$, including the relevant soft graviton contributions.
Boundary conditions at the past and future of ${\mathscr I}^\pm$ and a correspondingly modified Dirac bracket are required.

Built on

H. Bondi, M. G. J. van der Burg, A. W. K. Metzner, “Gravitational waves in general relativity VII. Waves from isolated axisymmetric systems”, Proc. Roy. Soc. Lond. A 269, 21 (1962); R. K. Sachs, “Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time”, Proc. Roy. Soc. Lond. A 270, 103 (1962)
1962
Earlier work this paper cites.
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
1987
Earlier work this paper cites.
D. Christodoulou and S. Klainerman, “The Global nonlinear stability of the Minkowski space,” Princeton University Press, Princeton, 1993
1993
Earlier work this paper cites.

Similar

S. Weinberg, “Infrared photons and gravitons,” Phys. Rev. 140
1995
Cited alongside, same era.
S. Y. Choi, J. S. Shim, H. S. Song, “Factorization and polarization in linearized gravity,” Phys. Rev. D 51
1995
Cited alongside, same era.
A. Strominger, “On BMS invariance of gravitational scattering”, arXiv:1312.2229 [hep-th]
Original
Cited in the paper.
A. Strominger, “Asymptotic Symmetries of Yang-Mills Theory,” arXiv:1308.0589 [hep-th]
Original
Cited in the paper.
See footnote 18 in T. Banks, “A Critique of pure string theory: Heterodox opinions of diverse dimensions,” hep-th/0306074
Cited in the paper.

Then

G. Barnich and C. Troessaert, “Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited,” Phys. Rev. Lett. 105
Original
2011
Later among the works it cites.
J. Maldacena and A. Zhiboedov, ”Notes on Soft Factors” unpublished (2012) and private communication
2012
Later among the works it cites.

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