Skip to main content
SpringerLink
Log in

Stability of a non-commutative Jackiw–Teitelboim gravity

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

Abstract

We start with a non-commutative version of the Jackiw–Teitelboim gravity in two dimensions which has a linear potential for the dilaton fields. We study whether it is possible to deform this model by adding quadratic terms to the potential but preserving the number of gauge symmetries. We find that no such deformation exists (provided one does not twist the gauge symmetries).

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. D. Grumiller, W. Kummer, D.V. Vassilevich, Phys. Rept. 369, 327 (2002) [arXiv:hep-th/0204253]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. E. Witten, Phys. Rev. D 44, 314 (1991); G. Mandal, A.M. Sengupta, S.R. Wadia, Mod. Phys. Lett. A 6, 1685 (1991); S. Elitzur, A. Forge, E. Rabinovici, Nucl. Phys. B 359, 581 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. C. Teitelboim, Phys. Lett. B 126, 41 (1983); in: Quantum Theory Of Gravity, p. 327–344, ed. by S. Christensen, (Adam Hilgar, Bristol, 1983)

    Article  MathSciNet  ADS  Google Scholar 

  4. R. Jackiw, in: Quantum Theory Of Gravity, p. 403–420, ed. by S. Christensen (Adam Hilgar, Bristol, 1983); Nucl. Phys. B 252, 343 (1985)

    Article  Google Scholar 

  5. B.M. Barbashov, V.V. Nesterenko, A.M. Chervyakov, Theor. Math. Phys. 40, 572 (1979) [Teor. Mat. Fiz. 40, 15 (1979)]

    Article  MathSciNet  Google Scholar 

  6. M.O. Katanaev, W. Kummer, H. Liebl, Phys. Rev. D 53, 5609 (1996) [arXiv:gr-qc/9511009]

    Article  MathSciNet  ADS  Google Scholar 

  7. W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 493, 491 (1997) [arXiv:gr-qc/9612012]; Nucl. Phys. B 544, 403 (1999) [arXiv:hep-th/9809168]; D. Grumiller, W. Kummer, D.V. Vassilevich, Nucl. Phys. B 580, 438 (2000) [arXiv:gr-qc/0001038]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. M.A. Rieffel, in: Deformation Quantization for Actions of ℝd. Memoirs Amer. Soc. 506, Providence, RI, 1993

  9. P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Schupp, J. Wess, Class. Quantum Gravity 22, 3511 (2005) [arXiv:hep-th/0504183]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. B.M. Zupnik, in: Reality in Non-commutative Gravity, arXiv:hep-th/0512231

  11. M. Chaichian, P.P. Kulish, K. Nishijima, A. Tureanu, Phys. Lett. B 604, 98 (2004) [arXiv:hep-th/0408069]; M. Chaichian, P. Presnajder, A. Tureanu, Phys. Rev. Lett. 94, 151602 (2005) [arXiv:hep-th/0409096]

    Article  MathSciNet  ADS  Google Scholar 

  12. J. Wess, Deformed Coordinate Spaces: Derivatives, arXiv:hep-th/0408080

  13. S. Cacciatori, A.H. Chamseddine, D. Klemm, L. Martucci, W.A. Sabra, D. Zanon, Class. Quantum Gravity 19, 4029 (2002) [arXiv:hep-th/0203038]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. D.V. Vassilevich, Nucl. Phys. B 715, 695 (2005) [arXiv:hep-th/0406163]

    Article  MathSciNet  ADS  Google Scholar 

  15. D.V. Vassilevich, Constraints, Gauge Symmetries, and Noncommutative Gravity in Two Dimensions, to appear in Theor. Math. Phys. [arXiv:hep-th/0502120]

  16. A.M. Ghezelbash, S. Parvizi, Nucl. Phys. B 592, 408 (2001) [arXiv:hep-th/0008120]

    Article  MathSciNet  ADS  Google Scholar 

  17. D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints (Springer, Berlin, 1990)

  18. M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992)

  19. D.M. Gitman, I.V. Tyutin, J. Phys. A: Math. Gen. 38, 5581 (2005) [hep-th/0409206]; Int. J. Mod. Phys. A 21, 327 (2006) [hep-th/0503218]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. R. Marnelius, Phys. Rev. D 10, 2535 (1974); J. Llosa, J. Vives, J. Math. Phys. 35, 2856 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  21. R.P. Woodard, Phys. Rev. A 62, 052105 (2000) [arXiv:hep-th/0006207]; J. Gomis, K. Kamimura, J. Llosa, Phys. Rev. D 63, 045003 (2001) [arXiv:hep-th/0006235]

    Article  ADS  Google Scholar 

  22. D. Grumiller, W. Kummer, D.V. Vassilevich, J. Phys. 48, 329 (2003) [arXiv:hep-th/0301061]

    MathSciNet  Google Scholar 

  23. F. Lizzi, S. Vaidya, P. Vitale, Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory, arXiv:hep-th/0601056

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009, Leipzig, Germany

    D.V. Vassilevich

  2. V.A. Fock Institute of Physics, St. Petersburg University, St. Petersburg, Russia

    D.V. Vassilevich

  3. Instituto de Física, Unversidade de São Paulo, São Paulo, Brasil

    R. Fresneda & D.M. Gitman

Authors
  1. D.V. Vassilevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Fresneda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D.M. Gitman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D.V. Vassilevich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vassilevich, D., Fresneda, R. & Gitman, D. Stability of a non-commutative Jackiw–Teitelboim gravity. Eur. Phys. J. C 47, 235–240 (2006). https://doi.org/10.1140/epjc/s2006-02544-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2006-02544-4

Keywords

Search

Navigation