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Constructing the cubic interaction vertex of higher spin gauge fields

I. L. Buchbinder1,*, Angelos Fotopoulos2,3,†, Anastasios C. Petkou2,‡, and Mirian Tsulaia2,§

  • 1Department of Theoretical Physics, Tomsk State Pedagogical University, 634041 Tomsk, Russia
  • 2Department of Physics, University of Crete, 710 03 Heraklion, Crete, Greece
  • 3Dipartimento di Fisica Teorica dell’Università di Torino and Istituto Nazionale di Fisica Nucleare, Sezione di Torino via P.Giuria 1, I-10125 Torino, Italy

  • *Electronic address: afotopou@tspu.edu.ru
  • †Electronic address: afotopou@physics.uoc.gr
  • ‡Electronic address: petkou@physics.uoc.gr
  • §Electronic address: tsulaia@physics.uoc.gr
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Phys. Rev. D 74, 105018 – Published 21 November, 2006

DOI: https://doi.org/10.1103/PhysRevD.74.105018

Abstract

We propose a method of construction of a cubic interaction in massless higher spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the higher spin gauge theory and generalize the higher spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction. The generators of this new algebra carry indexes which label the three higher spin fields involved into the cubic interaction. The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions. This method can in principle be applied for constructing the higher spin interaction vertex at any order. Our results are a first step towards the construction of a Lagrangian for interacting higher spin gauge fields that can be holographically studied.

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References (37)

  1. M. A. Vasiliev, Fortschr. Phys. 52, 702 (2004); X. Bekaert, S. Cnockaert, C. Iazeolla, and M. A. Vasiliev, hep-th/0503128; D. Sorokin, AIP Conf. Proc. 767, 172 (2005); N. Bouatta, G. Compere, and A. Sagnotti, hep-th/0409068; D. Francia and A. Sagnotti, J. Phys.: Conf. Ser. 33, 57 (2006); M. Bianchi and V. Didenko, hep-th/0502220; A. C. Petkou, hep-th/0410116; I. A. Bandos, AIP Conf. Proc. 767, 141 (2005).
  2. E. S. Fradkin and M. A. Vasiliev, Nucl. Phys. B291, 141 (1987); Ann. Phys. (N.Y.) 177, 63 (1987); Phys. Lett. B 189, 89 (1987).
  3. M. A. Vasiliev, Phys. Lett. B 243, 378 (1990); Nucl. Phys. B616, 106 (2001); B652, 407(E) (2003); Phys. Lett. B 257, 111 (1991); 285, 225 (1992); Classical Quantum Gravity 8, 1387 (1991); Phys. Lett. B 567, 139 (2003).
  4. E. Sezgin and P. Sundell, J. High Energy Phys. 09 (2001) 036; 09 (2001) 025; 07 (2002) 055; J. Engquist, E. Sezgin, and P. Sundell, Classical Quantum Gravity 19, 6175 (2002).
  5. S. W. MacDowell and F. Mansouri, Phys. Rev. Lett. 38, 739 (1977); 38, 1376(E) (1977); K. S. Stelle and P. C. West, Phys. Rev. D 21, 1466 (1980).
  6. C. Fronsdal, Phys. Rev. D 18, 3624 (1978).
  7. C. Fronsdal, Phys. Rev. D 20, 848 (1979).
  8. R. R. Metsaev, Classical Quantum Gravity 11, L141 (1994); hep-th/9810231; hep-th/0609029.
  9. I. L. Buchbinder, A. Pashnev, and M. Tsulaia, Phys. Lett. B 523, 338 (2001); hep-th/0206026.
  10. A. Sagnotti and M. Tsulaia, Nucl. Phys. B682, 83 (2004); A. Fotopoulos, K. L. Panigrahi, and M. Tsulaia, hep-th/0607248.
  11. D. Francia and A. Sagnotti, Phys. Lett. B 543, 303 (2002); 624, 93 (2005).
  12. D. Francia and A. Sagnotti, Classical Quantum Gravity 20, S473 (2003).
  13. F. A. Berends, G. J. H. Burgers, and H. van Dam, Nucl. Phys. B260, 295 (1985).
  14. A. K. H. Bengtsson, I. Bengtsson, and L. Brink, Nucl. Phys. B227, 41 (1983).
  15. R. R. Metsaev, hep-th/0512342; Mod. Phys. Lett. A 6, 359 (1991); 6, 2411 (1991); E. S. Fradkin and R. R. Metsaev, Classical Quantum Gravity 8, L89 (1991).
  16. X. Bekaert, N. Boulanger, and S. Cnockaert, J. High Energy Phys. 01 (2006) 052; X. Bekaert, N. Boulanger, S. Cnockaert, and S. Leclercq, Fortschr. Phys. 54, 282 (2006); N. Boulanger, S. Leclercq, and S. Cnockaert, Phys. Rev. D 73, 065019 (2006).
  17. A. K. H. Bengtsson, Classical Quantum Gravity 5, 437 (1988).
  18. I. G. Koh and S. Ouvry, Phys. Lett. B 179, 115 (1986); 183, 434(E) (1987).
  19. B. Sundborg, Nucl. Phys. B, Proc. Suppl. 102, 113 (2001).
  20. I. R. Klebanov and A. M. Polyakov, Phys. Lett. B 550, 213 (2002).
  21. A. C. Petkou, J. High Energy Phys. 03 (2003) 049.
  22. N. Moeller and P. West, Nucl. Phys. B729, 1 (2005); G. Bonelli, B669, 159 (2003); U. Lindstrom and M. Zabzine, Phys. Lett. B 584, 178 (2004); G. Bonelli, J. High Energy Phys. 11 (2003) 028.
  23. D. J. Gross and P. F. Mende, Nucl. Phys. B303, 407 (1988).
  24. E. Sezgin and P. Sundell, Nucl. Phys. B644, 303 (2002); B660, 403(E) (2003).
  25. M. Bianchi, J. F. Morales, and H. Samtleben, J. High Energy Phys. 07 (2003) 062; N. Beisert, M. Bianchi, J. F. Morales, and H. Samtleben, 02 (2004) 001; 07 (2004) 058.
  26. R. Gopakumar, Phys. Rev. D 70, 025009 (2004); C. Germani and A. Kehagias, Nucl. Phys. B725, 15 (2005); T. Saitou, J. High Energy Phys. 06 (2006) 010.
  27. J. Engquist and P. Sundell, Nucl. Phys. B752, 206 (2006).
  28. A. Pashnev and M. Tsulaia, Mod. Phys. Lett. A 13, 1853 (1998).
  29. C. Burdik, A. Pashnev, and M. Tsulaia, Mod. Phys. Lett. A 16, 731 (2001); Nucl. Phys. B, Proc. Suppl. 102, 285 (2001).
  30. I. L. Buchbinder, V. A. Krykhtin, and A. Pashnev, Nucl. Phys. B711, 367 (2005); X. Bekaert, I. L. Buchbinder, A. Pashnev, and M. Tsulaia, Classical Quantum Gravity 21, S1457 (2004); I. L. Buchbinder and V. A. Krykhtin, Nucl. Phys. B727, 537 (2005); I. L. Buchbinder, V. A. Krykhtin, L. L. Ryskina, and H. Takata, B711, 367 (2005).
  31. G. Barnich, N. Bouatta, and M. Grigoriev, J. High Energy Phys. 10 (2005) 010.
  32. A. Neveu and P. C. West, Nucl. Phys. B278, 601 (1986).
  33. D. J. Gross and A. Jevicki, Nucl. Phys. B283, 1 (1987); B287, 225 (1987).
  34. L. Brink, R. R. Metsaev, and M. A. Vasiliev, Nucl. Phys. B586, 183 (2000).
  35. K. B. Alkalaev, O. V. Shaynkman, and M. A. Vasiliev, hep-th/0601225; J. High Energy Phys. 08 (2005) 069.
  36. I. L. Buchbinder, V. A. Krykhtin, and P. M. Lavrov, hep-th/0608005.
  37. H. Osborn and A. C. Petkou, Ann. Phys. (N.Y.) 231, 311 (1994).

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Phys. Rev. D 74, 105018– Published 21 November, 2006
  • Received 6 October 2006

© 2006 American Physical Society

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