New symmetries for the gravitational S-matrix

Open Access
Regular Article - Theoretical Physics


In [15] we proposed a generalization of the BMS group \( \mathcal{G} \) which is a semi-direct product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, \( \mathcal{G} \) is a symmetry group of asymptotically flat space times. By taking \( \mathcal{G} \) as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S2) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S2) charges which we could not derive from first principles as \( \mathcal{G} \) does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S2) charges. The result of this paper, in conjunction with the results of [4, 15] prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to \( \mathcal{G} \).


Classical Theories of Gravity Space-Time Symmetries Gauge Symmetry 


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.


  1. [1]
    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].ADSCrossRefMATHGoogle Scholar
  2. [2]
    R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinbergs soft graviton theorem, arXiv:1401.7026 [INSPIRE].
  5. [5]
    S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
  7. [7]
    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].ADSGoogle Scholar
  8. [8]
    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].ADSGoogle Scholar
  9. [9]
    D.J. Gross and R. Jackiw, Low-Energy Theorem for Graviton Scattering, Phys. Rev. 166 (1968) 1287 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    S.G. Naculich and H.J. Schnitzer, Eikonal methods applied to gravitational scattering amplitudes, JHEP 05 (2011) 087 [arXiv:1101.1524] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S-matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    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].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    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].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    A. Ashtekar, Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity, J. Math. Phys. 22 (1981) 2885 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    A. Ashtekar, Quantization of the Radiative Modes of the Gravitational Field, In Quantum Gravity 2, C.J. Isham, R. Penrose and D.W. Sciama eds., Oxford University Press, Oxford U.K. (1981).Google Scholar
  20. [20]
    A. Ashtekar, Asymptotic Quantization, Bibliopolis, Naples, Italy (1987).MATHGoogle Scholar
  21. [21]
    A. Ashtekar, Geometry and Physics of Null Infinity, arXiv:1409.1800 [INSPIRE].
  22. [22]
    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 (1991).Google Scholar
  23. [23]
    J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    A. Ashtekar and A. Magnon-Ashtekar On the symplectic structure of general relativity, Commun. Math. Phys. 86 (1982) 55.ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    R. Geroch, Asymptotic structure of space-time, in Asymptotic structure of space-time, L. Witten ed., Plenum, New York U.S.A. (1976).Google Scholar
  26. [26]
    C. Kozameh and E.T. Newman, A note on asymptotically flat spaces. II, Gen. Rel. Grav. 15.5 (1983) 475.ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Instituto de Física, Facultad de CienciasMontevideoUruguay
  2. 2.Chennai Mathematical InstituteSiruseriIndia

Personalised recommendations