Advertisement

Journal of High Energy Physics

, 2014:112 | Cite as

New symmetries of massless QED

  • Temple He
  • Prahar Mitra
  • Achilleas P. PorfyriadisEmail author
  • Andrew Strominger
Open Access
Article

Abstract

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function \( \varepsilon \left(z,\overline{z}\right) \) on the conformal sphere at future null infinity ( Open image in new window ) but are independent of the retarded time. The value of ε at past null infinity ( Open image in new window ) is determined from that on Open image in new window by the condition that it take the same value at either end of any light ray crossing Minkowski space. The ε ≠ constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

Keywords

Spontaneous Symmetry Breaking Scattering Amplitudes Gauge Symmetry 

Notes

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.

References

  1. [1]
    A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinbergs soft graviton theorem, arXiv:1401.7026 [INSPIRE].
  4. [4]
    F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
  5. [5]
    E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes, arXiv:1404.5551 [INSPIRE].
  6. [6]
    B.U.W. Schwab and A. Volovich, Subleading soft theorem in arbitrary dimension from scattering equations, Phys. Rev. Lett. 113 (2014) 101601 [arXiv:1404.7749] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    Z. Bern, S. Davies and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons, arXiv:1405.1015 [INSPIRE].
  8. [8]
    S. He, Y.-t. Huang and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity, arXiv:1405.1410 [INSPIRE].
  9. [9]
    A.J. Larkoski, Conformal Invariance of the Subleading Soft Theorem in Gauge Theory, arXiv:1405.2346 [INSPIRE].
  10. [10]
    F. Cachazo and E.Y. Yuan, Are Soft Theorems Renormalized?, arXiv:1405.3413 [INSPIRE].
  11. [11]
    N. Afkhami-Jeddi, Soft Graviton Theorem in Arbitrary Dimensions, arXiv:1405.3533 [INSPIRE].
  12. [12]
    T. Adamo, E. Casali and D. Skinner, Perturbative gravity at null infinity, arXiv:1405.5122 [INSPIRE].
  13. [13]
    Y. Geyer, A.E. Lipstein and L. Mason, Ambitwistor strings at null infinity and subleading soft limits, arXiv:1406.1462 [INSPIRE].
  14. [14]
    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
  15. [15]
    B.U.W. Schwab, Subleading Soft Factor for String Disk Amplitudes, JHEP 08 (2014) 062 [arXiv:1406.4172] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M. Bianchi, S. He, Y.-t. Huang and C. Wen, More on Soft Theorems: Trees, Loops and Strings, arXiv:1406.5155 [INSPIRE].
  17. [17]
    A.P. Balachandran, S. Kurkcuoglu, A.R. de Queiroz and S. Vaidya, Spontaneous Lorentz Violation: The Case of Infrared QED, arXiv:1406.5845 [INSPIRE].
  18. [18]
    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
  19. [19]
    Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance, arXiv:1406.6987 [INSPIRE].
  20. [20]
    S. Weinberg, Infrared photons and gravitons, Phys. Rev. B 140 (1965) 516.ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge Univ. Pr., U.K., 1995.Google Scholar
  22. [22]
    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].ADSCrossRefzbMATHGoogle Scholar
  23. [23]
    R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    A. Ashtekar, Asymptotic Quantization: Based On 1984 Naples Lectures, Bibliopolis, Naples, Italy, 1987.zbMATHGoogle Scholar
  25. [25]
    C.D. White, Diagrammatic insights into next-to-soft corrections, arXiv:1406.7184 [INSPIRE].
  26. [26]
    D.R. Yennie, S.C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes, Annals Phys. 13 (1961) 379 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    J. Grammer, G. and D.R. Yennie, Improved treatment for the infrared divergence problem in quantum electrodynamics, Phys. Rev. D 8 (1973) 4332 [INSPIRE].
  28. [28]
    J. Maldacena and A. Zhiboedov, Notes on Soft Factors, unpublished and private communication, 2012.Google Scholar
  29. [29]
    V.P. Frolov, Null Surface Quantization and Quantum Field Theory in Asymptotically Flat Space-Time, Fortsch. Phys. 26 (1978) 455 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An Effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].ADSGoogle Scholar
  31. [31]
    I. Feige and M.D. Schwartz, Hard-Soft-Collinear Factorization to All Orders, arXiv:1403.6472 [INSPIRE].
  32. [32]
    P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [INSPIRE].CrossRefzbMATHGoogle Scholar
  33. [33]
    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].ADSCrossRefGoogle Scholar
  34. [34]
    S. Caron-Huot, When does the gluon reggeize?, arXiv:1309.6521 [INSPIRE].
  35. [35]
    V. Lysov, S. Pasterski and A. Strominger, Lows Subleading Soft Theorem as a Symmetry of QED, to appear.Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Temple He
    • 1
  • Prahar Mitra
    • 1
  • Achilleas P. Porfyriadis
    • 1
    Email author
  • Andrew Strominger
    • 1
  1. 1.Center for the Fundamental Laws of NatureHarvard UniversityCambridgeUnited Kingdom

Personalised recommendations