Advertisement

Scalar asymptotic charges and dual large gauge transformations

  • Miguel Campiglia
  • Laurent Freidel
  • Florian Hopfmueller
  • Ronak M. SoniEmail author
Open Access
Regular Article - Theoretical Physics
  • 22 Downloads

Abstract

In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical generators of large gauge symmetries. Such a symmetry interpretation has been so far missing for scalar soft theorems. We remedy this situation by treating the massless scalar field in terms of a dual two-form gauge field. We show that the asymptotic charges associated to the scalar soft theorem can be understood as generators of large gauge transformations of the dual two-form field.

The dual picture introduces two new puzzles: the charges have very unexpected Poisson brackets with the fields, and the monopole term does not always have a dual gauge transformation interpretation. We find analogues of these two properties in the Kramers-Wannier duality on a finite lattice, indicating that the free scalar theory has new edge modes at infinity that canonically commute with all the bulk degrees of freedom.

Keywords

Duality in Gauge Field Theories Gauge Symmetry Global Symmetries Scattering Amplitudes 

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, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
  2. [2]
    A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    D. Kapec, M. Perry, A.-M. Raclariu and A. Strominger, Infrared divergences in QED, revisited, Phys. Rev. D 96 (2017) 085002 [arXiv:1705.04311] [INSPIRE].
  4. [4]
    D. Carney, L. Chaurette, D. Neuenfeld and G. Semenoff, On the need for soft dressing, JHEP 09 (2018) 121 [arXiv:1803.02370] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    H. Afshar, E. Esmaeili and M.M. Sheikh-Jabbari, Asymptotic symmetries in p-form theories, JHEP 05 (2018) 042 [arXiv:1801.07752] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    E. Lake, Higher-form symmetries and spontaneous symmetry breaking, arXiv:1802.07747 [INSPIRE].
  7. [7]
    A. Campoleoni, D. Francia and C. Heissenberg, Asymptotic symmetries and charges at null infinity: from low to high spins, EPJ Web Conf. 191 (2018) 06011 [arXiv:1808.01542] [INSPIRE].
  8. [8]
    G. Satishchandran and R.M. Wald, The asymptotic behaviour of massless fields and the memory effect, arXiv:1901.05942 [INSPIRE].
  9. [9]
    M. Campiglia, L. Coito and S. Mizera, Can scalars have asymptotic symmetries?, Phys. Rev. D 97 (2018) 046002 [arXiv:1703.07885] [INSPIRE].
  10. [10]
    M. Campiglia and L. Coito, Asymptotic charges from soft scalars in even dimensions, Phys. Rev. D 97 (2018) 066009 [arXiv:1711.05773] [INSPIRE].
  11. [11]
    Y. Hamada and S. Sugishita, Soft pion theorem, asymptotic symmetry and new memory effect, JHEP 11 (2017) 203 [arXiv:1709.05018] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
  13. [13]
    T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, JHEP 09 (2016) 102 [arXiv:1601.04744] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    H. Afshar, E. Esmaeili and M.M. Sheikh-Jabbari, String memory effect, JHEP 02 (2019) 053 [arXiv:1811.07368] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    A. Strominger, Magnetic corrections to the soft photon theorem, Phys. Rev. Lett. 116 (2016) 031602 [arXiv:1509.00543] [INSPIRE].
  17. [17]
    Y. Hamada, M.-S. Seo and G. Shiu, Electromagnetic duality and the electric memory effect, JHEP 02 (2018) 046 [arXiv:1711.09968] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    V. Hosseinzadeh, A. Seraj and M.M. Sheikh-Jabbari, Soft charges and electric-magnetic duality, JHEP 08 (2018) 102 [arXiv:1806.01901] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    L. Freidel and D. Pranzetti, Electromagnetic duality and central charge, Phys. Rev. D 98 (2018) 116008 [arXiv:1806.03161] [INSPIRE].
  20. [20]
    M. Henneaux and C. Troessaert, Asymptotic structure of a massless scalar field and its dual two-form field at spatial infinity, arXiv:1812.07445 [INSPIRE].
  21. [21]
    E. Di Grezia and S. Esposito, Minimal coupling of the Kalb-Ramond field to a scalar field, Int. J. Theor. Phys. 43 (2004) 445 [hep-th/0304058] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    D. Kapec, M. Pate and A. Strominger, New symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    I.R. Klebanov and L. Susskind, Continuum strings from discrete field theories, Nucl. Phys. B 309 (1988) 175 [INSPIRE].
  24. [24]
    K. Konishi, G. Paffuti and P. Provero, Minimum physical length and the generalized uncertainty principle in string theory, Phys. Lett. B 234 (1990) 276 [INSPIRE].
  25. [25]
    H. Casini and M. Huerta, Entanglement entropy for a Maxwell field: numerical calculation on a two dimensional lattice, Phys. Rev. D 90 (2014) 105013 [arXiv:1406.2991] [INSPIRE].
  26. [26]
    D. Radičević, Entanglement entropy and duality, JHEP 11 (2016) 130 [arXiv:1605.09396] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  27. [27]
    U. Moitra, R.M. Soni and S.P. Trivedi, Entanglement entropy, relative entropy and duality, arXiv:1811.06986 [INSPIRE].
  28. [28]
    H.A. Kramers and G.H. Wannier, Statistics of the two-dimensional ferromagnet. Part II, Phys. Rev. 60 (1941) 263 [INSPIRE].
  29. [29]
    H.A. Kramers and G.H. Wannier, Statistics of the two-dimensional ferromagnet. Part I, Phys. Rev. 60 (1941) 252 [INSPIRE].
  30. [30]
    J.B. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys. 51 (1979) 659 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de Física, Facultad de CienciasMontevideoUruguay
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Department of Theoretical Physics, Tata Institute of Fundamental ResearchMumbaiIndia
  4. 4.Stanford Institute for Theoretical PhysicsStanfordU.S.A.

Personalised recommendations