Advertisement

On the elimination of infinitesimal Gribov ambiguities in non-Abelian gauge theories

  • Antônio D. PereiraJr.
  • Rodrigo F. SobreiroEmail author
Regular Article - Theoretical Physics

Abstract

An alternative method to account for the Gribov ambiguities in gauge theories is presented. It is shown that, to eliminate Gribov ambiguities, at infinitesimal level, it is required to break the BRST symmetry in a soft manner. This can be done by introducing a suitable extra constraint that eliminates the infinitesimal Gribov copies. It is shown that the present approach is consistent with the well established known cases in the literature, i.e., the Landau and maximal Abelian gauges. The method is valid for gauges depending exclusively on the gauge field and is restricted to classical level. However, occasionally, we deal with quantum aspects of the technique, which are used to improve the results.

Keywords

Zero Mode Landau Gauge Auxiliary Field BRST Transformation Ghost Propagator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors are grateful to M.A.L. Capri, M.S. Guimarães, D. Dudal, S.A. Dias and L. Bonora for very useful discussions. The Conselho Nacional de Desenvolvimento Científico e Tecnológico12 (CNPq-Brazil), The Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and the Pró-Reitoria de Pesquisa, Pós-Graduação e Inovação (PROPPI-UFF) are acknowledged for financial support.

References

  1. 1.
    V.N. Gribov, Nucl. Phys. B 139, 1 (1978) MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    L.D. Faddeev, V.N. Popov, Phys. Lett. B 25, 29 (1967) ADSCrossRefGoogle Scholar
  3. 3.
    R.F. Sobreiro, S.P. Sorella, Introduction to the Gribov ambiguities in Euclidean Yang–Mills theories, in Lectures given at 13th Jorge Andre Swieca Summer School on Particle and Fields, Campos do Jordao, Brazil, 9–22 January, 2005. E-print: arXiv:hep-th/0504095 Google Scholar
  4. 4.
    I.M. Singer, Commun. Math. Phys. 60, 7 (1978) ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. 1 (Wiley, New York, 1963) zbMATHGoogle Scholar
  6. 6.
    M. Daniel, C.M. Viallet, Rev. Mod. Phys. 52, 175 (1980) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    P. Cotta-Ramusino, C. Reina, J. Geom. Phys. 1(3), 121–155 (1985) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    G. Falqui, C. Reina, Commun. Math. Phys. 102, 503 (1985) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    M. Nakahara, Geometry, Topology and Physics. Graduate Student Series in Physics (Hilger, Bristol, 1990), 505 pp. CrossRefzbMATHGoogle Scholar
  10. 10.
    R.A. Bertlmann, Anomalies in Quantum Field Theory. International Series of Monographs on Physics, vol. 91 (Clarendon, Oxford, 1996), 566 pp. zbMATHGoogle Scholar
  11. 11.
    D. Zwanziger, Nucl. Phys. B 323, 513 (1989) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    G. Dell’Antonio, D. Zwanziger, Nucl. Phys. B 326, 333 (1989) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    G. Dell’Antonio, D. Zwanziger, Commun. Math. Phys. 138, 291 (1991) MathSciNetADSCrossRefzbMATHGoogle Scholar
  14. 14.
    D. Zwanziger, Nucl. Phys. B 399, 477 (1993) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    N. Maggiore, M. Schaden, Phys. Rev. D 50, 6616 (1994). arXiv:hep-th/9310111 ADSCrossRefGoogle Scholar
  16. 16.
    D. Dudal, R.F. Sobreiro, S.P. Sorella, H. Verschelde, Phys. Rev. D 72, 014016 (2005). arXiv:hep-th/0502183 ADSCrossRefGoogle Scholar
  17. 17.
    D. Dudal, J.A. Gracey, S.P. Sorella, N. Vandersickel, H. Verschelde, Phys. Rev. D 78, 065047 (2008). arXiv:0806.4348 [hep-th] ADSCrossRefGoogle Scholar
  18. 18.
    D. Dudal, S.P. Sorella, N. Vandersickel, Phys. Rev. D 84, 065039 (2011). arXiv:1105.3371 [hep-th] ADSCrossRefGoogle Scholar
  19. 19.
    M.A.L. Capri, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, R. Thibes, Phys. Rev. D 72, 085021 (2005). hep-th/0507052 ADSCrossRefGoogle Scholar
  20. 20.
    M.A.L. Capri, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, R. Thibes, Phys. Rev. D 74, 105007 (2006). hep-th/0609212 MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    M.A.L. Capri, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, R. Thibes, Phys. Rev. D 77, 105023 (2008). arXiv:0801.0566 [hep-th] ADSCrossRefGoogle Scholar
  22. 22.
    M.A.L. Capri, A.J. Gomez, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, Phys. Rev. D 79, 025019 (2009). arXiv:0811.2760 [hep-th] ADSCrossRefGoogle Scholar
  23. 23.
    M.A.L. Capri, A.J. Gomez, M.S. Guimaraes, V.E.R. Lemes, S.P. Sorella, J. Phys. A 43, 245402 (2010). arXiv:1002.1659 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    I.L. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker, A. Sternbeck, Proc. Sci. LAT2007, 290 (2007). arXiv:0710.1968 [hep-lat] Google Scholar
  25. 25.
    A. Cucchieri, T. Mendes, Proc. Sci. LAT2007, 297 (2007). arXiv:0710.0412 [hep-lat] Google Scholar
  26. 26.
    A. Sternbeck, L. von Smekal, D.B. Leinweber, A.G. Williams Proc. Sci. LAT2007, 340 (2007). arXiv:0710.1982 [hep-lat]
  27. 27.
    A. Cucchieri, T. Mendes, Phys. Rev. D 81, 016005 (2010). arXiv:0904.4033 [hep-lat] ADSCrossRefGoogle Scholar
  28. 28.
    L. Baulieu, S.P. Sorella, Phys. Lett. B 671, 481 (2009). arXiv:0808.1356 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    L. Baulieu, M.A.L. Capri, A.J. Gomez, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, Eur. Phys. J. C 66, 451 (2010). arXiv:0901.3158 [hep-th] ADSCrossRefGoogle Scholar
  30. 30.
    O. Piguet, S.P. Sorella, Lect. Notes Phys., M Monogr. 28, 1–134 (1995) MathSciNetCrossRefGoogle Scholar
  31. 31.
    N. Vandersickel, arXiv:1104.1315 [hep-th]
  32. 32.
    A. Cucchieri, D. Dudal, T. Mendes, N. Vandersickel, Phys. Rev. D 85, 094513 (2012). arXiv:1111.2327 [hep-lat] ADSCrossRefGoogle Scholar
  33. 33.
    J. Serreau, M. Tissier, Phys. Lett. B 712, 97 (2012). arXiv:1202.3432 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    P. van Baal, Nucl. Phys. B 369, 259 (1992) ADSCrossRefGoogle Scholar
  35. 35.
    A.A. Slavnov, J. High Energy Phys. 0808, 047 (2008). arXiv:0807.1795 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    A. Quadri, A.A. Slavnov, J. High Energy Phys. 1007, 087 (2010). arXiv:1002.2490 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    D. Zwanziger, Nucl. Phys. B 518, 237 (1998) ADSCrossRefzbMATHGoogle Scholar
  38. 38.
    M.A.L. Capri, A.J. Gomez, M.S. Guimaraes, V.E.R. Lemes, S.P. Sorella, D.G. Tedesco, Phys. Rev. D 82, 105019 (2010). arXiv:1009.4135 [hep-th] ADSCrossRefGoogle Scholar
  39. 39.
    Work in progress Google Scholar
  40. 40.
    D. Dudal, J.A. Gracey, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, R. Thibes, H. Verschelde, J. High Energy Phys. 0507, 059 (2005). hep-th/0505037 MathSciNetADSCrossRefGoogle Scholar
  41. 41.
    M.A.L. Capri, R.F. Sobreiro, S.P. Sorella, Phys. Rev. D 73, 041701 (2006). hep-th/0512096 MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    M.A.L. Capri, R.F. Sobreiro, S.P. Sorella, R. Thibes, Ann. Phys. 322, 1776 (2007). hep-th/0607117 MathSciNetADSCrossRefzbMATHGoogle Scholar
  43. 43.
    G. Curci, R. Ferrari, Nuovo Cimento A 35, 1 (1976). Erratum, ibid. 47, 555 (1978) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Instituto de Física, Campus da Praia VermelhaUFF—Universidade Federal FluminenseNiteróiBrazil

Personalised recommendations