Abstract
BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (\( \mathrm{\mathcal{I}} \) +). BMS− transformations similarly act on ingoing data at past null infinity (\( \mathrm{\mathcal{I}} \) −). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link \( \mathrm{\mathcal{I}} \) + to \( \mathrm{\mathcal{I}} \) − and thereby identify “diagonal” elements BMS0 of BMS+ × BMS−. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity \( \mathcal{S} \)-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S 2 at \( \mathrm{\mathcal{I}} \). The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of \( \mathrm{\mathcal{I}} \).
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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 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. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press, Cambridge U.K. (1995).
P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [INSPIRE].
J. Ware, R. Saotome and R. Akhoury, Construction of an asymptotic S matrix for perturbative quantum gravity, JHEP 10 (2013) 159 [arXiv:1308.6285] [INSPIRE].
D. Christodoulou and S. Klainerman, The Global nonlinear stability of the Minkowski space, Princeton University Press, Princeton U.S.A. (1993).
T. He, V. Lysov, P. Mitra and A. Strominger, BMS Supertranslations and Weinberg’s Soft Graviton Theorem, arXiv:1401.7026 [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, Supertranslations call for superrotations, PoS(CNCFG2010)010 [arXiv:1102.4632] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
T. Banks, A Critique of pure string theory: Heterodox opinions of diverse dimensions, hep-th/0306074 [INSPIRE].
A.P. Balachandran and S. Vaidya, Spontaneous Lorentz Violation in Gauge Theories, Eur. Phys. J. Plus 128 (2013) 118 [arXiv:1302.3406] [INSPIRE].
J. Maldacena and A. Zhiboedov, Notes on Soft Factors, unpublished (2012) and private communication.
A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, arXiv:1308.0589 [INSPIRE].
G. Barnich and P.-H. Lambert, Einstein- Yang-Mills theory: Asymptotic symmetries, Phys. Rev. D 88 (2013) 103006 [arXiv:1310.2698] [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].
R.M. Wald, General Relativity, Chicago University Press, Chicago U.S.A. (1984).
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
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Strominger, A. On BMS invariance of gravitational scattering. J. High Energ. Phys. 2014, 152 (2014). https://doi.org/10.1007/JHEP07(2014)152
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DOI: https://doi.org/10.1007/JHEP07(2014)152