Self-completeness and spontaneous dimensional reduction

Abstract

A viable quantum theory of gravity is one of the biggest challenges physicists are facing. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity —spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it does not. In such a way we established an “exclusive disjunction” or “exclusive or” (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of the Einstein gravity.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    J. Ambjorn, J. Jurkiewicz, R. Loll, Phys. Rev. Lett. 95, 171301 (2005) hep-th/0505113.

    ADS  Article  Google Scholar 

  2. 2.

    O. Lauscher, M. Reuter, JHEP 10, 050 (2005) hep-th/0508202.

    MathSciNet  ADS  Article  Google Scholar 

  3. 3.

    D. Benedetti, Phys. Rev. Lett. 102, 111303 (2009) arXiv:0811.1396.

    MathSciNet  ADS  Article  Google Scholar 

  4. 4.

    L. Modesto, Class. Quantum Grav. 26, 242002 (2009) arXiv:0812.2214.

    MathSciNet  ADS  Article  Google Scholar 

  5. 5.

    P. Nicolini, E. Spallucci, Phys. Lett. B 695, 290 (2011) arXiv:1005.1509.

    ADS  Article  Google Scholar 

  6. 6.

    J. Laiho, D. Coumbe, Phys. Rev. Lett. 107, 161301 (2011) arXiv:1104.5505.

    ADS  Article  Google Scholar 

  7. 7.

    G. Calcagni, Phys. Rev. E 87, 012123 (2013) arXiv:1205.5046 [hep-th].

    ADS  Article  Google Scholar 

  8. 8.

    G. Calcagni, Phys. Rev. D 86, 044021 (2012) arXiv:1204.2550 [hep-th].

    ADS  Article  Google Scholar 

  9. 9.

    L. Modesto, P. Nicolini, Phys. Rev. D 81, 104040 (2010) arXiv:0912.0220.

    ADS  Article  Google Scholar 

  10. 10.

    S. Carlip, Spontaneous dimensional reduction in short-distance quantum gravity?, invited talk at the 25th Max Born Symposium: “The Planck Scale” - 29 Jun - 3 Jul 2009, Wroclaw, Poland, arXiv:0909.3329.

  11. 11.

    S. Carlip, The Small Scale Structure of Spacetime, in Foundations of Space and Time, edited by George Ellis, Jeff Murugan, Amanda Weltman (Cambridge University Press, 2011) arXiv:1009.1136.

  12. 12.

    S. Carlip, D. Grumiller, Phys. Rev. D 84, 084029 (2011) arXiv:1108.4686.

    ADS  Article  Google Scholar 

  13. 13.

    J. Mureika, Phys. Lett. B 716, 171 (2012) arXiv:1204.3619 [gr-qc].

    ADS  Article  Google Scholar 

  14. 14.

    Lhc physics data taking gets underway at new record collision energy of 8 tev (2012) http://press.web.cern.ch/press/PressReleases/Releases2012/PR10.12E.html.

  15. 15.

    A. Aurilia, E. Spallucci, Planck’s uncertainty principle and the saturation of Lorentz boosts by Planckian black holes, http://www.csupomona.edu/ aaurilia/planck.html (2004).

  16. 16.

    R.J. Adler, Am. J. Phys. 78, 925 (2010) arXiv:1001.1205.

    ADS  Article  Google Scholar 

  17. 17.

    G. Dvali, C. Gomez, Self-Completeness of Einstein Gravity, arXiv:1005.3497.

  18. 18.

    G. Dvali, S. Folkerts, C. Germani, Phys. Rev. D 84, 024039 (2011) arXiv:1006.0984.

    ADS  Article  Google Scholar 

  19. 19.

    A. Bonanno, M. Reuter, Phys. Rev. D 62, 043008 (2000) hep-th/0002196.

    ADS  Article  Google Scholar 

  20. 20.

    P. Nicolini, J. Phys. A 38, L631 (2005) hep-th/0507266.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  21. 21.

    P. Nicolini, A. Smailagic, E. Spallucci, Phys. Lett. B 632, 547 (2006) gr-qc/0510112.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  22. 22.

    L. Modesto, Class. Quantum Grav. 23, 5587 (2006) gr-qc/0509078.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  23. 23.

    L. Modesto, Int. J. Theor. Phys. 47, 357 (2008) gr-qc/0610074.

    MathSciNet  Article  MATH  Google Scholar 

  24. 24.

    E. Spallucci, A. Smailagic, P. Nicolini, Phys. Lett. B 670, 449 (2009) arXiv:0801.3519.

    MathSciNet  ADS  Article  Google Scholar 

  25. 25.

    P. Nicolini, Int. J. Mod. Phys. A 24, 1229 (2009) arXiv:0807.1939.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  26. 26.

    P. Nicolini, E. Spallucci, Class. Quantum Grav. 27, 015010 (2010) arXiv:0902.4654.

    MathSciNet  ADS  Article  Google Scholar 

  27. 27.

    L. Modesto, J.W. Moffat, P. Nicolini, Phys. Lett. B 695, 397 (2011) arXiv:1010.0680.

    MathSciNet  ADS  Article  Google Scholar 

  28. 28.

    B. Carr, L. Modesto, I. Premont-Schwarz, Generalized Uncertainty Principle and Self-dual Black Holes, arXiv:1107.0708.

  29. 29.

    L. Modesto, Phys. Rev. D 86, 044005 (2012) arXiv:1107.2403 [hep-th].

    ADS  Article  Google Scholar 

  30. 30.

    L. Modesto, Super-renormalizable Higher-Derivative Quantum Gravity, arXiv:1202.0008.

  31. 31.

    P. Nicolini, Nonlocal and generalized uncertainty principle black holes, arXiv:1202.2102.

  32. 32.

    E. Spallucci, S. Ansoldi, Phys. Lett. B 701, 471 (2011) arXiv:1101.2760.

    MathSciNet  ADS  Article  Google Scholar 

  33. 33.

    E. Spallucci, A. Smailagic, Phys. Lett. B 709, 266 (2012) arXiv:1202.1686.

    MathSciNet  ADS  Article  Google Scholar 

  34. 34.

    R. Mann, J. Mureika, Phys. Lett. B 703, 167 (2011) arXiv:1105.5925.

    MathSciNet  ADS  Article  Google Scholar 

  35. 35.

    J. Mureika, P. Nicolini, E. Spallucci, Phys. Rev. D 85, 106007 (2012) arXiv:1111.5830.

    ADS  Article  Google Scholar 

  36. 36.

    R. Casadio, O. Micu, A. Orlandi, Eur. Phys. J. C 72, 2146 (2012) arXiv:1205.6303 [hep-th].

    ADS  Article  Google Scholar 

  37. 37.

    G.’t Hooft, Dimensional reduction in quantum gravity, in Salam Fest (World Scientific Co. Singapore, 1993) gr-qc/9310026, essay dedicated to Abdus Salam.

  38. 38.

    D. Grumiller, W. Kummer, D. Vassilevich, Phys. Rep. 369, 327 (2002) hep-th/0204253.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  39. 39.

    D. Grumiller, R. Meyer, Turk. J. Phys. 30, 349 (2006) hep-th/0604049.

    Google Scholar 

  40. 40.

    R.B. Mann, S. Ross, Class. Quantum Grav. 10, 1405 (1993) gr-qc/9208004.

    MathSciNet  ADS  Article  Google Scholar 

  41. 41.

    R. Jackiw, Theor. Math. Phys. 148, 941 (2006) hep-th/0511065.

    MathSciNet  Article  MATH  Google Scholar 

  42. 42.

    D. Grumiller, R. Jackiw, Liouville gravity from Einstein gravity, in Recent developments in theoretical physics, edited by S. Gosh, G. Kar (World Scientific, Singapore, 2010) p. 331, arXiv:0712.3775.

  43. 43.

    R.B. Mann, A. Shiekh, L. Tarasov, Nucl. Phys. B 341, 134 (1990).

    ADS  Article  Google Scholar 

  44. 44.

    A.E. Sikkema, R.B. Mann, Class. Quantum Grav. 8, 219 (1991).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  45. 45.

    R.B. Mann, S. Morsink, A. Sikkema, T. Steele, Phys. Rev. D 43, 3948 (1991).

    MathSciNet  ADS  Article  Google Scholar 

  46. 46.

    S.M. Morsink, R.B. Mann, Class. Quantum Grav. 8, 2257 (1991).

    MathSciNet  ADS  Article  Google Scholar 

  47. 47.

    R.B. Mann, T.G. Steele, Class. Quantum Grav. 9, 475 (1992).

    MathSciNet  ADS  Article  Google Scholar 

  48. 48.

    R. Jackiw, Liouville field theory: a two-dimensional model for gravity?, in Quantum Theory Of Gravity, edited by S. Christensen (Adam Hilgar, Bristol, 1984) pp. 403--420.

  49. 49.

    D. Cangemi, R. Jackiw, Phys. Rev. Lett. 69, 233 (1992) hep-th/9203056.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  50. 50.

    R.B. Mann, Nucl. Phys. B 418, 231 (1994) hep-th/9308034.

    ADS  Article  MATH  Google Scholar 

  51. 51.

    J.R. Mureika, P. Nicolini, Phys. Rev. D 84, 044020 (2011) arXiv:1104.4120.

    ADS  Article  Google Scholar 

  52. 52.

    M. Banados, C. Teitelboim, J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992) hep-th/9204099.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  53. 53.

    X. Calmet, G. Landsberg, Lower Dimensional Quantum Black Holes, arXiv:1008.3390.

  54. 54.

    CMS Collaboration (V. Khachatryan et al.), Phys. Lett. B 697, 434 (2011) arXiv:1012.3375.

    ADS  Article  Google Scholar 

  55. 55.

    CMS Collaboration (S. Chatrchyan et al.), JHEP 04, 061 (2012) arXiv:1202.6396.

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jonas Mureika.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mureika, J., Nicolini, P. Self-completeness and spontaneous dimensional reduction. Eur. Phys. J. Plus 128, 78 (2013). https://doi.org/10.1140/epjp/i2013-13078-0

Download citation

Keywords

  • Black Hole
  • Dimensional Reduction
  • Quantum Gravity
  • Planck Scale
  • Einstein Gravity