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Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT

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Abstract

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.

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References

  1. DeWitt, B.: In: DeWitt, B., DeWitt, C. (eds.) Relativity, Groups and Topology. Gordon & Breach, New York (1964)

    Google Scholar 

  2. DeWitt, B.: Phys. Rev. 160, 1113 (1967)

    Article  MATH  ADS  Google Scholar 

  3. DeWitt, B.: Phys. Rev. 162, 1195 (1967) 1239

    Article  ADS  Google Scholar 

  4. ’t Hooft, G., Veltman, M.: Ann. Inst. Henri Poincare XX, 69 (1974)

    MathSciNet  Google Scholar 

  5. Veltman, M.: Methods in Field Theory. Les Houches. North-Holland, Amsterdam (1976)

    Google Scholar 

  6. Weinberg, S.: In: Hawking, S., Israel, W. (eds.) General Relativity, an Einstein Centenary Survey. Cambridge University Press, Cambridge (1979)

    Google Scholar 

  7. Utiyama, R., DeWitt, B.: J. Math. Phys. 3, 608 (1962)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Deser, S.: In: Arnowitt, R., Nath, P. (eds.) Proceedings of the Conference on Gauge Theories and Modern Field Theories. MIT Press, Cambridge (1975)

    Google Scholar 

  9. Weinberg, S.: In: Smith, J.R. (ed.) Proceedings of the XVIIth International Conference on High Energy Physics. Rutherford Laboratory, Chilton, Didcot (1974)

    Google Scholar 

  10. Stelle, K.: Phys. Rev. D 16, 953 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  11. Stelle, K.: Gen. Relativ. Gravit. 9, 353 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  12. Julve, J., Tonin, M.: Nuovo Cimento B 46, 137 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  13. Tomboulis, E.: Phys. Lett. B 70, 361 (1977)

    Article  ADS  Google Scholar 

  14. Tomboulis, E.: Phys. Lett. B 97, 77 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  15. Fradkin, E., Tseytlin, A.: Nucl. Phys. B 201, 469 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  16. Fradkin, E., Tseytlin, A.: Phys. Rep. 119, 233 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  17. Hamada, K.: Prog. Theor. Phys. 108, 399 (2002)

    Article  MATH  ADS  Google Scholar 

  18. Hamada, K.: Conformal Field Theory on R×S 3 from Quantized Gravity. arXiv:0811.1647[hep-th]

  19. Hamada, K., Horata, S., Yukawa, T.: In: Focus on Quantum Gravity Research. Nova Publ., New York (2006), Chap. 1.

    Google Scholar 

  20. Wess, J., Zumino, B.: Phys. Lett. B 37, 95 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  21. Capper, D., Duff, M.: Nuovo Cimento A 23, 173 (1974)

    Article  ADS  Google Scholar 

  22. Deser, S., Duff, M., Isham, C.: Nucl. Phys. B 111, 45 (1976)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. Duff, M.: Nucl. Phys. B 125, 334 (1977)

    Article  ADS  Google Scholar 

  24. Duff, M.: Class. Quantum Gravity 11, 1387 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  25. Polyakov, A.: Phys. Lett. B 103, 207 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  26. Polyakov, A.: Mod. Phys. Lett. A 2, 893 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  27. Knizhnik, V., Polyakov, A., Zamolodchikov, A.: Mod. Phys. Lett. A 3, 819 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  28. Distler, J., Kawai, H.: Nucl. Phys. B 321, 509 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  29. David, F.: Mod. Phys. Lett. A 3, 1651 (1988)

    Article  ADS  Google Scholar 

  30. Seiberg, N.: Prog. Theor. Phys. Suppl. 102, 319 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  31. Riegert, R.: Phys. Lett. B 134, 56 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  32. Antoniadis, I., Mottola, E.: Phys. Rev. D 45, 2013 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  33. Antoniadis, I., Mazur, P., Mottola, E.: Nucl. Phys. B 388, 627 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  34. Antoniadis, I., Mazur, P., Mottola, E.: Phys. Rev. D 55, 4756 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  35. Antoniadis, I., Mazur, P., Mottola, E.: Phys. Rev. D 55, 4770 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  36. Hamada, K., Sugino, F.: Nucl. Phys. B 553, 283 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. Hamada, K., Horata, S.: Prog. Theor. Phys. 110, 1169 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. Hamada, K.: Int. J. Mod. Phys. A 20, 5353 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  39. ’t Hooft, G., Veltman, M.: Nucl. Phys. B 44, 189 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  40. Bonora, L., Cotta-Ramusino, P., Reina, C.: Phys. Lett. B 126, 305 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  41. Hathrell, S.: Ann. Phys. 142, 34 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  42. Hathrell, S.: Ann. Phys. 139, 136 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  43. Freeman, M.: Ann. Phys. 153, 339 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  44. Hamada, K., Yukawa, T.: Mod. Phys. Lett. A 20, 509 (2005)

    Article  MATH  ADS  Google Scholar 

  45. Hamada, K., Horata, S., Yukawa, T.: Phys. Rev. D 74, 123502 (2006)

    Article  ADS  Google Scholar 

  46. Hamada, K., Horata, S., Sugiyama, N., Yukawa, T.: Prog. Theor. Phys. 119, 253 (2008)

    Article  ADS  Google Scholar 

  47. Hamada, K., Minamizaki, A., Sugamoto, A.: Mod. Phys. Lett. A 23, 237 (2008)

    Article  ADS  Google Scholar 

  48. Kugo, T., Ojima, I.: Prog. Theor. Phys. Suppl. 66, 1 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  49. Drummond, I., Hathrell, S.: Phys. Rev. D 21, 958 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  50. Gell-Mann, M., Low, F.: Phys. Rev. 95, 1300 (1954)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  51. Symanzik, K.: Commun. Math. Phys. 18, 227 (1970)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  52. Callan, C. Jr.: Phys. Rev. D 2, 1541 (1970)

    Article  ADS  Google Scholar 

  53. ’t Hooft, G.: Nucl. Phys. B 61, 455 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  54. Weinberg, S.: Phys. Rev. D 8, 3497 (1973)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Particle and Nuclear Studies, KEK, Tsukuba, 305-0801, Japan

    Ken-ji Hamada

  2. Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies (Sokendai), Tsukuba, 305-0801, Japan

    Ken-ji Hamada

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  1. Ken-ji Hamada
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Correspondence to Ken-ji Hamada.

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Hamada, Kj. Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT. Found Phys 39, 1356–1393 (2009). https://doi.org/10.1007/s10701-009-9358-x

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  • DOI: https://doi.org/10.1007/s10701-009-9358-x

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