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More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s)

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Abstract

In this paper we provide strong evidence that there is no ambiguity in the choice of the horizon function underlying the Gribov–Zwanziger action. We show that there is only one correct possibility which is determined by the requirement of multiplicative renormalizability. As a consequence, this means that relations derived from other horizon functions cannot be given a consistent interpretation in terms of a local and renormalizable quantum field theory. In addition, we also discuss that the Kugo–Ojima functions u(p 2) and w(p 2) can only be defined after renormalization of the underlying Green function(s).

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References

  1. V.N. Gribov, Nucl. Phys. B 139, 1 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  2. D. Zwanziger, Nucl. Phys. B 323, 513 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  3. G. Dell’Antonio, D. Zwanziger, Nucl. Phys. B 326, 333 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  4. D. Zwanziger, Nucl. Phys. B 399, 477 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  5. D. Zwanziger, Phys. Rev. D 65, 094039 (2002)

    Article  ADS  Google Scholar 

  6. J.A. Gracey, Phys. Lett. B 632, 282 (2006)

    Article  ADS  Google Scholar 

  7. F.R. Ford, J.A. Gracey, J. Phys. A 42, 325402 (2009)

    Article  MathSciNet  Google Scholar 

  8. K.I. Kondo, arXiv:0909.4866 [hep-th]

  9. K.I. Kondo, arXiv:0907.3249 [hep-th]

  10. K.I. Kondo, Phys. Lett. B 678, 322 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  11. A. Cucchieri, T. Mendes, PoS LAT2007, 297 (2007)

    Google Scholar 

  12. A. Cucchieri, T. Mendes, Phys. Rev. D 78, 094503 (2008)

    Article  ADS  Google Scholar 

  13. V.G. Bornyakov, V.K. Mitrjushkin, M. Muller-Preussker, Phys. Rev. D 79, 074504 (2009)

    ADS  Google Scholar 

  14. I.L. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker, A. Sternbeck, Phys. Lett. B 676, 69 (2009)

    ADS  Google Scholar 

  15. A. Maas, Phys. Rev. D 79, 014505 (2009)

    Article  ADS  Google Scholar 

  16. A. Maas, arXiv:0907.5185 [hep-lat]

  17. A. Maas, J.M. Pawlowski, D. Spielmann, A. Sternbeck, L. von Smekal, arXiv:0912.4203 [hep-lat]

  18. C.S. Fischer, A. Maas, J.M. Pawlowski, Ann. Phys. 324, 2408 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. O. Oliveira, P.J. Silva, PoS LAT2007, 332 (2007)

    Google Scholar 

  20. P.J. Silva, O. Oliveira, AIP Conf. Proc. 892, 220 (2007)

    Article  ADS  Google Scholar 

  21. D. Dudal, S.P. Sorella, N. Vandersickel, H. Verschelde, Phys. Rev. D 77, 071501 (2008)

    ADS  Google Scholar 

  22. D. Dudal, J.A. Gracey, S.P. Sorella, N. Vandersickel, H. Verschelde, Phys. Rev. D 78, 065047 (2008)

    ADS  Google Scholar 

  23. Ph. Boucaud, J.P. Leroy, A.L. Yaouanc, J. Micheli, O. Pene, J. Rodriguez-Quintero, J. High Energy Phys. 0806, 012 (2008)

    Article  ADS  Google Scholar 

  24. Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez-Quintero, J. High Energy Phys. 0806, 099 (2008)

    Article  ADS  Google Scholar 

  25. A.C. Aguilar, D. Binosi, J. Papavassiliou, Phys. Rev. D 78, 025010 (2008)

    ADS  Google Scholar 

  26. A.C. Aguilar, D. Binosi, J. Papavassiliou, J. Rodriguez-Quintero, Phys. Rev. D 80, 085018 (2009)

    ADS  Google Scholar 

  27. M.Q. Huber, R. Alkofer, S.P. Sorella, Phys. Rev. D 81, 065003 (2010)

    ADS  Google Scholar 

  28. T. Kugo, I. Ojima, Prog. Theor. Phys. Suppl. 66, 1 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  29. T. Kugo, arXiv:hep-th/9511033

  30. D. Dudal, R.F. Sobreiro, S.P. Sorella, H. Verschelde, Phys. Rev. D 72, 014016 (2005)

    ADS  Google Scholar 

  31. D. Dudal, S.P. Sorella, N. Vandersickel, H. Verschelde, J. High Energy Phys. 0908, 110 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  32. D. Zwanziger, Nucl. Phys. B 412, 657 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. D. Dudal, S.P. Sorella, N. Vandersickel, H. Verschelde, Phys. Rev. D 79, 121701 (2009)

    MathSciNet  ADS  Google Scholar 

  34. D. Dudal, V.E.R. Lemes, M.S. Sarandy, S.P. Sorella, M. Picariello, A. Vicini, J.A. Gracey, H. Verschelde, J. High Energy Phys. 0306, 003 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  35. P.A. Grassi, T. Hurth, A. Quadri, Phys. Rev. D 70, 105014 (2004)

    MathSciNet  ADS  Google Scholar 

  36. Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez-Quintero, Phys. Rev. D 80, 094501 (2009)

    ADS  Google Scholar 

  37. D. Dudal, S.P. Sorella, N. Vandersickel, H. Verschelde, work in progress

  38. D. Dudal, O. Oliveira, N. Vandersickel, arXiv:1002.2374 [hep-lat]

  39. M.A.L. Capri, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella, R. Thibes, Ann. Phys. 323, 752 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  40. N. Maggiore, M. Schaden, Phys. Rev. D 50, 6616 (1994)

    Article  ADS  Google Scholar 

  41. O. Piguet, S.P. Sorella, Lect. Notes Phys. M 28, 1 (1995)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium

    D. Dudal & N. Vandersickel

  2. Departamento de Física Teórica, Instituto de Física, UERJ—Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Maracanã, Rio de Janeiro, Brasil

    S. P. Sorella

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  1. D. Dudal
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  2. S. P. Sorella
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  3. N. Vandersickel
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Correspondence to N. Vandersickel.

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Dudal, D., Sorella, S.P. & Vandersickel, N. More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s). Eur. Phys. J. C 68, 283–298 (2010). https://doi.org/10.1140/epjc/s10052-010-1304-8

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  • DOI: https://doi.org/10.1140/epjc/s10052-010-1304-8

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