- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Super-renormalizable quantum gravity

Leonardo Modesto

  • Perimeter Institute for Theoretical Physics, 31 Caroline Street, Waterloo, Ontario N2L 2Y5, Canada

PDF

Phys. Rev. D 86, 044005 – Published 3 August, 2012

DOI: https://doi.org/10.1103/PhysRevD.86.044005

Abstract

In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers from the unitarity problem because of the presence of a ghost (state of negative norm) in the theory. In this paper, we reconsider the theory first introduced by Tomboulis in 1997, but we expand and extensively study it at both the classical and quantum level. This theory is ghost-free, since the introduction of (in general) two entire functions in the model with the property does not introduce new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to the lowest order in the mass scale of the theory. Any truncation of the entire functions gives rise to the unitarity violation, but if we keep all the infinite series, we do not fall into these troubles. The theory is renormalizable at one loop and finite from two loops on. Since only one-loop Feynman diagrams are divergent, then the theory is super-renormalizable. We analyze the fractal properties of the theory at high energy showing a reduction of the spacetime dimension at short scales. Black hole spherical symmetric solutions are also studied omitting the high curvature corrections in the equation of motions. The solutions are regular and the classical singularity is replaced by a “de Sitter-like core” in r=0. Black holes may show a “multihorizon” structure depending on the value of the mass. We conclude the paper with a generalization of the Tomboulis theory to a multidimensional spacetime.

View figure in article

Article Text

References (70)

  1. K. S. Stelle, Phys. Rev. D 16, 953 (1977).
  2. J. W. Moffat, Phys. Rev. D 41, 1177 (1990); B. J. Hand and J. W. Moffat, 43, 1896 (1991); D. Evens, J. W. Moffat, G. Kleppe, and R. P. Woodard, 43, 499 (1991); N. J. Cornish, Mod. Phys. Lett. A 7, 1895 (1992); Int. J. Mod. Phys. A 7, 6121 (1992).
  3. N. J. Cornish, Mod. Phys. Lett. A 7, 631 (1992); J. W. Moffat, Eur. Phys. J. Plus 126, 43 (2011).
  4. E. T. Tomboulis, arXiv:hep-th/9702146v1.
  5. A. O. Barvinsky, Phys. Lett. B 710, 12 (2012); Phys. Rev. D 71, 084007 (2005); Phys. Lett. B 572, 109 (2003); H. W. Hamber and R. M. Williams, Phys. Rev. D 72, 044026 (2005); N. Arkani-Hamed, S. Dimopoulos, G. Dvali, and G. Gabadadze, arXiv:hep-th/0209227v1; G. Calcagni and G. Nardelli, J. High Energy Phys. 02 (2010) 093.
  6. L. Crane and L. Smolin, Nucl. Phys. B267, 714 (1986).
  7. O. Lauscher and M. Reuter, J. High Energy Phys. 10 (2005) 050; D. Benedetti, Pedro F. Machado, and F. Saueressig, Mod. Phys. Lett. A 24, 2233 (2009).
  8. D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, United Kingdom, 2000); J. Ambjorn, J. Jurkiewicz, and R. Loll, Phys. Lett. B 607, 205 (2005).
  9. L. Modesto, Classical Quantum Gravity 26, 242002 (2009).
  10. S. Carlip, in XXV Max Born Symposium, “Physics at the Planck scale,” Wroclaw, Poland (2009) (to be published), arXiv:0909.3329.
  11. D. Benedetti, Phys. Rev. Lett. 102, 111303 (2009).
  12. L. Modesto and Piero Nicolini, Phys. Rev. D 81, 104040 (2010).
  13. L. Modesto, Classical Quantum Gravity 26, 242002 (2009).
  14. L. Modesto, arXiv:0905.1665.
  15. F. Caravelli and L. Modesto, arXiv:0905.2170.
  16. E. Magliaro, C. Perini, and L. Modesto, arXiv:0911.0437.
  17. G. Calcagni, Phys. Rev. Lett. 104, 251301 (2010).
  18. G. Calcagni, J. High Energy Phys. 03 (2010)120.
  19. G. Calcagni, Phys. Lett. B 697, 251 (2011).
  20. G. Calcagni, Phys. Rev. D 84, 061501 (2011); arXiv:1106.5787.
  21. L. Anchordoqui, De Chang Dai, M. Fairbairn, G. Landsberg, and D. Stojkovic, Mod. Phys. Lett. A 27, 1250021-1 (2012); J. R. Mureika and D. Stojkovic, Phys. Rev. Lett. 106, 101101 (2011).
  22. L. Modesto, J. W. Moffat, and P. Nicolini, Phys. Lett. B 695, 397 (2011).
  23. A. Smailagic and E. Spallucci, J. Phys. A 36, L467 (2003).
  24. A. Smailagic and E. Spallucci, J. Phys. A 36, L517 (2003).
  25. A. Smailagic and E. Spallucci, J. Phys. A 37, 7169 (2004).
  26. S. Alexander, A. Marciano, and L. Modesto, Phys. Rev. D 85, 124030 (2012).
  27. I. L. Buchbinder, Sergei D. Odintsov, and I. L. Shapiro, Effective Action in Quantum Gravity (Taylor & Francis, London, 1992).
  28. P. Van Nieuwenhuizen, Nucl. Phys. B60, 478 (1973).
  29. M. Asorey, J. L. Lopez, and I. L. Shapiro, Int. J. Mod. Phys. A 12, 5711 (1997).
  30. P. Nicolini, A. Smailagic, and E. Spallucci, in Proceedings of EPS 13 General Conference—“Beyond Einstein, Physics for the 21st Century,” 2005 (University of Bern, Bern, Switzerland) [hep-th/0507226].
  31. P. Nicolini, J. Phys. A 38, L631 (2005).
  32. P. Nicolini, A. Smailagic, and E. Spallucci, Phys. Lett. B 632, 547 (2006).
  33. T. G. Rizzo, J. High Energy Phys. 09 (2006) 021.
  34. E. Spallucci, A. Smailagic, and P. Nicolini, Phys. Rev. D 73, 084004 (2006).
  35. S. Ansoldi, P. Nicolini, A. Smailagic, and E. Spallucci, Phys. Lett. B 645, 261 (2007).
  36. E. Spallucci, A. Smailagic, and P. Nicolini, Phys. Lett. B 670, 449 (2009).
  37. P. Nicolini, Int. J. Mod. Phys. A 24, 1229 (2009).
  38. R. Casadio and P. Nicolini, J. High Energy Phys. 11 (2008) 072.
  39. I. Arraut, D. Batic, and M. Nowakowski, Classical Quantum Gravity 26, 245006 (2009).
  40. P. Nicolini and E. Spallucci, Classical Quantum Gravity 27, 015010 (2010).
  41. A. Smailagic and E. Spallucci, Phys. Lett. B 688, 82 (2010).
  42. D. M. Gingrich, J. High Energy Phys. 05 (2010) 022.
  43. I. Arraut, D. Batic, and M. Nowakowski, J. Math. Phys. (N.Y.) 51, 022503 (2010).
  44. R. Banerjee, S. Gangopadhyay, and S. K. Modak, Phys. Lett. B 686, 181 (2010).
  45. P. Nicolini, Phys. Rev. D 82, 044030 (2010).
  46. L. Modesto and A. Randono, arXiv:1003.1998; F. Caravelli and L. Modesto, Phys. Lett. B 702, 307 (2011).
  47. L. Modesto and P. Nicolini, Phys. Rev. D 82, 104035 (2010).
  48. R. B. Mann and P. Nicolini, Phys. Rev. D 84, 064014 (2011).
  49. J. R. Mureika and P. Nicolini, Phys. Rev. D 84, 044020 (2011).
  50. J. Ambjorn, J. Jurkiewicz, and R. Loll, Phys. Rev. Lett. 95, 171301 (2005).
  51. D. V. Vassilevich, Phys. Rep. 388, 279 (2003).
  52. G. V. Efimov, Nonlocal Interactions of Quantized Fields (Nauka, Moscow, 1977).
  53. N. V. Krasnikov, Teor. Math. Fiz. 73, 235 (1986).
  54. N. Barnaby and N. Kamran, J. High Energy Phys. 02 (2008) 008; G. Calcagni, M. Montobbio, and G. Nardelli, Phys. Rev. D 76, 126001 (2007); Phys. Lett. B 662, 285 (2008).
  55. A. DeBenedictis, Can. J. Phys. 87, 255 (2009).
  56. P. Gaete, J. A. Helayel-Neto, and E. Spallucci, Phys. Lett. B 693, 155 (2010).
  57. A. Acciolyan and A. Azeredo, J. Math. Phys. (N.Y.) 43, 1 (2002).
  58. B. Hatfield, Quantum Field Theory of Point Particles and Strings (Addison-Wesley, Redwood City, CA, 1992).
  59. E. Witten, Nucl. Phys. B268, 253 (1986).
  60. L. Brekke, P. G. O. Freund, M. Olson, and E. Witten, Nucl. Phys. B302, 365 (1988).
  61. D. J. Gross and P. F. Mende, Phys. Lett. B 197, 129 (1987).
  62. Pei-Ming Ho, Classical Quantum Gravity 21, 2641 (2004).
  63. T. Biswas, J. Kapusta, and A. Reddy, arXiv:1201.1580.
  64. N. Barnaby, T. Biswas, and J. M. Cline, J. High Energy Phys. 04 (2007) 056.
  65. T. Biswas, A. Mazumdar, and W. Siegel, J. Cosmol. Astropart. Phys. 03 (2006) 009.
  66. T. Biswas, T. Koivisto, and A. Mazumdar, J. Cosmol. Astropart. Phys. 11 (2010) 008.
  67. V. A. Kostelecky and S. Samuel, Phys. Rev. D 42, 1289 (1990).
  68. A. S. Koshelev, Proceedings of BW2011 Workshop (to be published), arXiv:1112.6410.
  69. G. Calcagni and G. Nardelli, Phys. Rev. D 82, 123518 (2010); T. Biswas, T. Koivisto, and A. Mazumdar, J. Cosmol. Astropart. Phys. 11 (2010) 008.
  70. D. V. Shirkov, Phys. Part. Nucl. Lett. 7, 379 (2010).

Outline

Information

Phys. Rev. D 86, 044005– Published 3 August, 2012
  • Received 12 March 2012

© 2012 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation