Skip to main content
SpringerLink
Log in

Discussing quantum aspects of higher-derivative 3-D gravity in the first-order formalism

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

Abstract

In this paper, we reassess the issue of deriving the propagators and identifying the spectrum of excitations associated to the vielbein and spin connection of (1+2)-D gravity in the presence of dynamical torsion, while working in the first-order formulation. A number of peculiarities is pointed out whenever the Chern–Simons term is taken into account along with a combination of bilinear terms in the torsion tensor. We present a procedure to derive the full set of propagators, based on an algebra of enlarged spin-type operators, and we discuss under which conditions the poles of the tree-level 2-point functions correspond to physical excitations that do not conflict with causality and unitarity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Andringa, E.A. Bergshoeff, M. de Roo, O. Hohm, E. Sezgin, P.K. Townsend, Class. Quantum Gravity 27, 025010 (2010)

    Article  ADS  Google Scholar 

  2. H.I. Arcos, J.G. Pereira, Int. J. Mod. Phys. D 13, 2193 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. A.S. Belyaev, I.L. Shapiro, Phys. Lett. B 425, 246 (1998)

    Article  ADS  Google Scholar 

  4. E.A. Bergshoeff, O. Hohm, P.K. Townsend, Phys. Rev. Lett. 102, 201301 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  5. E.A. Bergshoeff, O. Hohm, P.K. Townsend, Phys. Rev. D 79, 124042 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  6. E. Bergshoeff, O. Hohm, P. Townsend, On massive gravitons in 2+1 dimensions. arXiv:0912.2944 [hep-th]

  7. J.L. Boldo, L.M. de Moraes, J.A. Helayel-Neto, Class. Quantum Gravity 17, 813 (2000)

    Article  MATH  ADS  Google Scholar 

  8. S.M. Carroll, G.B. Field, Phys. Rev. D 50, 3867 (1994)

    Article  ADS  Google Scholar 

  9. D.D.K. Chow, C.N. Pope, E. Sezgin, Kundt spacetimes as solutions of topologically massive gravity. arXiv:0912.3438 [hep-th]

  10. D. Dalmazi, Phys. Rev. D 80, 085008 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  11. D. Dalmazi, E.L. Mendonça, J. High Energy Phys. 0909, 011 (2009)

    Article  ADS  Google Scholar 

  12. L.M. de Moraes, J.A. Helayël-Neto, C. Hernaski, B. Pereira-Dias, A.A. Vargas Paredes, V.J. Vasquez, Otoya, Work in progress

  13. V. De Sabbata, M. Gasperini, Phys. Lett. A 77, 300 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  14. V. de Sabbata, M. Gasperini, Introduction to Gravitation (World Scientific, Singapore, 1985)

    Google Scholar 

  15. S. Deser, R. Jackiw, S. Templeton, Phys. Rev. Lett. 48, 975 (1982)

    Article  ADS  Google Scholar 

  16. S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 140, 372 (1982); [Erratum-ibid. 185, 406.1988 APNYA,281,409 (1988 APNYA,281,409-449.2000)]

    Article  MathSciNet  ADS  Google Scholar 

  17. M. Gurses, Killing vector fields in three dimensions: a method to solve massive gravity field equations. arXiv:1001.1039 [gr-qc]

  18. R.T. Hammond, Phys. Rev. D 52, 6918 (1995)

    Article  ADS  Google Scholar 

  19. F.W. Hehl, J.D. McCrea, E.W. Mielke, Y. Ne’eman, Phys. Rep. 258, 1 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  20. F.W. Hehl, P. Von Der Heyde, G.D. Kerlick, J.M. Nester, Rev. Mod. Phys. 48, 393 (1976)

    Article  ADS  Google Scholar 

  21. C.A. Hernaski, A.A. Vargas-Paredes, J.A. Helayel-Neto, Phys. Rev. D 80, 124012 (2009)

    Article  ADS  Google Scholar 

  22. E.W. Mielke, P. Baekler, Phys. Lett. A 156, 399 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  23. M. Nakasone, I. Oda, Phys. Rev. D 79, 104012 (2009)

    Article  ADS  Google Scholar 

  24. M. Nakasone, I. Oda, Prog. Theor. Phys. 121, 1389 (2009)

    Article  MATH  ADS  Google Scholar 

  25. F.C.P. Nunes, G.O. Pires, Phys. Lett. B 301, 339 (1993)

    Article  ADS  Google Scholar 

  26. R.J. Rivers, Nuovo Cimento 34, 387 (1964)

    MathSciNet  Google Scholar 

  27. E. Sezgin, Phys. Rev. D 24, 1677 (1981)

    Article  ADS  Google Scholar 

  28. E. Sezgin, P. van Nieuwenhuizen, Phys. Rev. D 21, 3269 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  29. I.L. Shapiro, Mod. Phys. Lett. A 9, 729 (1994)

    Article  ADS  Google Scholar 

  30. I.L. Shapiro, Phys. Rep. 357, 113 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. P. Van Nieuwenhuizen, Nucl. Phys. B 60, 478 (1973)

    Article  ADS  Google Scholar 

  32. J. Zanelli, (Super)-gravities beyond 4 dimensions. arXiv:hep-th/0206169

Download references

Author information

Authors and Affiliations

  1. CBPF, Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Urca, Rio de Janeiro, Brazil

    J. A. Helayël-Neto

  2. Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Av. Governador Roberto Silveira, 1900, Prado, Nova Friburgo, Rio de Janeiro, Brazil

    L. M. de Moraes

  3. UFF, Universidade Federal Fluminense, Campus da Praia Vermelha, Av. Gal. Milton Tavares de Souza, s/nº, Niteroi, Rio de Janeiro, Brazil

    V. J. Vasquez

Authors
  1. J. A. Helayël-Neto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. M. de Moraes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. J. Vasquez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. J. Vasquez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Helayël-Neto, J.A., de Moraes, L.M. & Vasquez, V.J. Discussing quantum aspects of higher-derivative 3-D gravity in the first-order formalism. Eur. Phys. J. C 67, 311–319 (2010). https://doi.org/10.1140/epjc/s10052-010-1297-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s10052-010-1297-3

Keywords

Search

Navigation