Journal of High Energy Physics

, 2014:128 | Cite as

Revisiting soliton contributions to perturbative amplitudes

Open Access


It is often said that soliton contributions to perturbative processes in QFT are exponentially suppressed by a form factor. We provide a derivation of this form factor by studying the soliton-antisoliton pair production amplitude for a class of scalar theories with generic soliton moduli. This reduces to the calculation of a matrix element in the quantum mechanics on the soliton moduli space. We investigate the conditions under which the latter leads to suppression. Extending this framework to instanton-solitons in five-dimensional Yang-Mills theory leaves open the possibility that such contributions will not be suppressed.


Scattering Amplitudes Solitons Monopoles and Instantons Nonperturbative Effects 


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]
    J. Le Guillou and J. Zinn-Justin, Large order behaviour of perturbation theory, Current Physics Sources and Comments volume 7, North-Holland, The Netherlands (1990).Google Scholar
  2. [2]
    A.K. Drukier and S. Nussinov, Monopole pair creation in energetic collisions: is it possible?, Phys. Rev. Lett. 49 (1982) 102 [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    C. Bachas, On the breakdown of perturbation theory, Theor. Math. Phys. 95 (1993) 491 [hep-th/9212033] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    T. Banks, Arguments against a finite N = 8 supergravity, arXiv:1205.5768 [INSPIRE].
  5. [5]
    S.R. Coleman, Crossing symmetry in semiclassical soliton scattering, Phys. Rev. D 12 (1975) 1650 [INSPIRE].ADSGoogle Scholar
  6. [6]
    M.R. Douglas, On D = 5 super Yang-Mills theory and (2, 0) theory, JHEP 02 (2011) 011 [arXiv:1012.2880] [INSPIRE].ADSGoogle Scholar
  7. [7]
    N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M5-branes, D4-branes and Quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  8. [8]
    Z. Bern et al., D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops, Phys. Rev. D 87 (2013) 025018 [arXiv:1210.7709] [INSPIRE].ADSGoogle Scholar
  9. [9]
    J. Goldstone and R. Jackiw, Quantization of nonlinear waves, Phys. Rev. D 11 (1975) 1486 [INSPIRE].ADSGoogle Scholar
  10. [10]
    G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  11. [11]
    N. Manton and P. Sutcliffe, Topological solitons, Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge U.K. (2004).Google Scholar
  12. [12]
    R. Rajaraman and E.J. Weinberg, Internal symmetry and the semiclassical method in quantum field theory, Phys. Rev. D 11 (1975) 2950 [INSPIRE].ADSGoogle Scholar
  13. [13]
    D. Bazeia, J.R.S. Nascimento, R.F. Ribeiro and D. Toledo, Soliton stability in systems of two real scalar fields, J. Phys. A 30 (1997) 8157 [hep-th/9705224] [INSPIRE].MathSciNetADSGoogle Scholar
  14. [14]
    G.P. de Brito and A. de Souza Dutra, Orbit based procedure for doublets of scalar fields and the emergence of triple kinks and other defects, Phys. Lett. B 736 (2014) 438 [arXiv:1405.5458] [INSPIRE].CrossRefADSGoogle Scholar
  15. [15]
    S.V. Demidov and D.G. Levkov, Soliton-antisoliton pair production in particle collisions, Phys. Rev. Lett. 107 (2011) 071601 [arXiv:1103.0013] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    S.V. Demidov and D.G. Levkov, Soliton pair creation in classical wave scattering, JHEP 06 (2011) 016 [arXiv:1103.2133] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix, Cambridge University Press, Cambridge U.K. (1966).MATHGoogle Scholar
  18. [18]
    C. Papageorgakis and A.B. Royston, Scalar soliton quantization with generic moduli, JHEP 06 (2014) 003 [arXiv:1403.5017] [INSPIRE].CrossRefADSGoogle Scholar
  19. [19]
    X.-D. Ji, A relativistic skyrmion and its form-factors, Phys. Lett. B 254 (1991) 456 [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    J.-L. Gervais, A. Jevicki and B. Sakita, Perturbation expansion around extended particle states in quantum field theory. 1, Phys. Rev. D 12 (1975) 1038 [INSPIRE].ADSGoogle Scholar
  21. [21]
    N. Dorey, M.P. Mattis and J. Hughes, Soliton quantization and internal symmetry, Phys. Rev. D 49 (1994) 3598 [hep-th/9309018] [INSPIRE].ADSGoogle Scholar
  22. [22]
    N. Dorey, J. Hughes and M.P. Mattis, Skyrmion quantization and the decay of the Delta, Phys. Rev. D 50 (1994) 5816 [hep-ph/9404274] [INSPIRE].ADSGoogle Scholar
  23. [23]
    C. Teitelboim, Proper time approach to the quantization of the gravitational field, Phys. Lett. B 96 (1980) 77 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  24. [24]
    M. Henneaux and C. Teitelboim, Relativistic quantum mechanics of supersymmetric particles, Annals Phys. 143 (1982) 127 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  25. [25]
    P.D. Mannheim, Klein-Gordon propagator via first quantization, Phys. Lett. B 166 (1986) 191 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  26. [26]
    S. Monaghan, BRS hamiltonian quantization of a spinless relativistic particle in relativistic gauges, Phys. Lett. B 178 (1986) 231 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  27. [27]
    C. Papageorgakis and A.B. Royston, A semiclassical relativistic form factor for the kink, in preparation.Google Scholar
  28. [28]
    P.H. Weisz, Exact quantum sine-Gordon soliton form-factors, Phys. Lett. B 67 (1977) 179 [INSPIRE].CrossRefADSGoogle Scholar
  29. [29]
    G. Holzwarth, Electromagnetic nucleon form-factors and their spectral functions in soliton models, Z. Phys. A 356 (1996) 339 [hep-ph/9606336] [INSPIRE].ADSGoogle Scholar
  30. [30]
    Y. Tachikawa, On S-duality of 5D super Yang-Mills on S 1, JHEP 11 (2011) 123 [arXiv:1110.0531] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  31. [31]
    N. Lambert, H. Nastase and C. Papageorgakis, 5D Yang-Mills instantons from ABJM monopoles, Phys. Rev. D 85 (2012) 066002 [arXiv:1111.5619] [INSPIRE].ADSGoogle Scholar
  32. [32]
    H.-C. Kim, S. Kim, E. Koh, K. Lee and S. Lee, On instantons as Kaluza-Klein modes of M5-branes, JHEP 12 (2011) 031 [arXiv:1110.2175] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  33. [33]
    D. Young, Wilson loops in five-dimensional super-Yang-Mills, JHEP 02 (2012) 052 [arXiv:1112.3309] [INSPIRE].CrossRefADSGoogle Scholar
  34. [34]
    J. Källén and M. Zabzine, Twisted supersymmetric 5D Yang-Mills theory and contact geometry, JHEP 05 (2012) 125 [arXiv:1202.1956] [INSPIRE].CrossRefADSGoogle Scholar
  35. [35]
    K. Hosomichi, R.-K. Seong and S. Terashima, Supersymmetric gauge theories on the five-sphere, Nucl. Phys. B 865 (2012) 376 [arXiv:1203.0371] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  36. [36]
    J. Källén, J. Qiu and M. Zabzine, The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere, JHEP 08 (2012) 157 [arXiv:1206.6008] [INSPIRE].CrossRefADSGoogle Scholar
  37. [37]
    H.-C. Kim and S. Kim, M5-branes from gauge theories on the 5-sphere, JHEP 05 (2013) 144 [arXiv:1206.6339] [INSPIRE].CrossRefADSGoogle Scholar
  38. [38]
    J. Källén, J.A. Minahan, A. Nedelin and M. Zabzine, N 3 -behavior from 5D Yang-Mills theory, JHEP 10 (2012) 184 [arXiv:1207.3763] [INSPIRE].CrossRefADSGoogle Scholar
  39. [39]
    D. Bak and A. Gustavsson, M5/D4 brane partition function on a circle bundle, JHEP 12 (2012) 099 [arXiv:1209.4391] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  40. [40]
    Y. Fukuda, T. Kawano and N. Matsumiya, 5D SYM and 2D q-deformed YM, Nucl. Phys. B 869 (2013) 493 [arXiv:1210.2855] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  41. [41]
    H.-C. Kim, J. Kim and S. Kim, Instantons on the 5-sphere and M5-branes, arXiv:1211.0144 [INSPIRE].
  42. [42]
    N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, Deconstructing (2, 0) proposals, Phys. Rev. D 88 (2013) 026007 [arXiv:1212.3337] [INSPIRE].ADSGoogle Scholar
  43. [43]
    D. Bak and A. Gustavsson, One dyonic instanton in 5D maximal SYM theory, JHEP 07 (2013) 021 [arXiv:1305.3637] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  44. [44]
    N.D. Lambert and D. Tong, Dyonic instantons in five-dimensional gauge theories, Phys. Lett. B 462 (1999) 89 [hep-th/9907014] [INSPIRE].CrossRefADSGoogle Scholar
  45. [45]
    K. Peeters and M. Zamaklar, Motion on moduli spaces with potentials, JHEP 12 (2001) 032 [hep-th/0107164] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  46. [46]
    J.P. Allen and D.J. Smith, The low energy dynamics of charge two dyonic instantons, JHEP 02 (2013) 113 [arXiv:1210.3208] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  47. [47]
    D. Bak, C.-k. Lee, K.-M. Lee and P. Yi, Low-energy dynamics for 1/4 BPS dyons, Phys. Rev. D 61 (2000) 025001 [hep-th/9906119] [INSPIRE].MathSciNetADSGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Constantinos Papageorgakis
    • 1
    • 2
  • Andrew B. Royston
    • 3
  1. 1.NHETC and Department of Physics and AstronomyRutgers UniversityPiscatawayU.S.A.
  2. 2.CRST and School of Physics and Astronomy, Queen MaryUniversity of LondonLondonU.K.
  3. 3.George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and AstronomyTexas A&M UniversityCollege StationU.S.A.

Personalised recommendations