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Curvature phase transition inR 2 quantum gravity and induction of Einstein gravity

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Abstract

The phase transition with respect to the curvature in the effective potential ofR 2 quantum gravity with matter is studied. The effective potential is calculated in the framework of the renormalization-group approach up to terms linear in the curvature. A universal expression is obtained for the induced gravitational and cosmological constants. The effective potential, and also the induced cosmological and gravitational constants depend on the relationships between the coupling constants of the original theory and on the gauge parameters. When the matter is represented by a single scalar field values fixed by asymptotic freedom are chosen for the coupling constants. There is no gauge dependence for the unified parametrization-and gauge-invariant effective action.

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References

  1. G. 't Hooft and M. Veltman,Ann. Inst. H. Poincaré,20, 69 (1974).

    Google Scholar 

  2. S. Deser and P. van Nieuwenhuizen,Phys. Rev.,100, 401 (1974).

    Google Scholar 

  3. K. S. Stelle,Phys. Rev. D,16, 953 (1977).

    Google Scholar 

  4. B. L. Voronov and I. V. Tyutin,Yad. Fiz.,39, 998 (1984).

    Google Scholar 

  5. A. Salam and J. Strathdee,Phys. Rev. D,18, 4480 (1978).

    Google Scholar 

  6. E. T. Tomboulis,Phys. Lett. B,70, 361 (1977);97, 77 (1980);Phys. Rev. Lett.,52, 1173 (1984).

    Google Scholar 

  7. I. Antoniadis and E. T. Tomboulis,Phys. Rev. D,33, 2756 (1986).

    Google Scholar 

  8. D. A. Johnston,Nucl. Phys. B,297, 721 (1988).

    Google Scholar 

  9. E. S. Fradkin and A. A. Tseytlin,Nucl. Phys. B,201, 469 (1982).

    Google Scholar 

  10. I. G. Avramidi and A. O. Barvinsky,Phys. Lett. B,159, 269 (1985).

    Google Scholar 

  11. I. G. Avramidi,Yad. Fiz.,44, 255 (1986).

    Google Scholar 

  12. S. L. Adler,Rev. Mod. Phys.,54, 729 (1982).

    Google Scholar 

  13. A. Zee,Ann. Phys. (N.Y.),151, 431 (1983).

    Google Scholar 

  14. R. I. Nepomechie,Phys. Lett. B,136, 33 (1984).

    Google Scholar 

  15. I. L. Bukhbinder,Izv. Vyssh. Uchebn. Zaved. Fiz., No. 3, 77 (1986).

    Google Scholar 

  16. I. L. Bukhbinder and S. D. Odintsov,Yad. Fiz.,42, 1268 (1985).

    Google Scholar 

  17. I. L. Bukhbinder and I. L. Shapiro,Yad. Fiz.,44, 1033 (1986).

    Google Scholar 

  18. I. L. Buchbinder, O. K. Kalashnikov, I. L. Shapiro, V. B. Vologodsky, and Yu. Yu. Wolfengaut,Fortschr. Phys.,37, 207 (1989).

    Google Scholar 

  19. I. L. Buchbinder, O. K. Kalashnikov, I. L. Shapiro, V. B. Vologodsky, and Yu. Yu. Wolfengaut,Phys. Lett. B,216, 127 (1989);Yad. Fiz.,49, 876 (1989).

    Google Scholar 

  20. I. L. Shapiro,Class. Quant. Grav.,6, 1197 (1989).

    Google Scholar 

  21. I. L. Buchbinder, S. D. Odintsov, and I. L. Shapiro,Riv. Nuovo Cimento,12, 1 (1989).

    Google Scholar 

  22. G. A. Vilkovisky,Nucl. Phys.,234, 125 (1984).

    Google Scholar 

  23. B. S. DeWitt, in:Architecture of Fundamental Interactions at Short Distances, North-Holland (1985).

  24. H. T. Cho, Norman Preprint (1990), p. 1.

  25. Yu. Yu. Vol'fengaut, I. L. Shapiro, and E. G. Yagunov,Izv. Vyssh. Uchebn. Zaved. Fiz., No. 1, 36 (1990).

    Google Scholar 

  26. L. Parker and D. J. Tomis,Phys. Rev. D,29, 1584 (1984).

    Google Scholar 

  27. I. L. Buchbinder, S. D. Odintsov, and O. A. Fonarev,Mod. Phys. Lett. A,4, 2713 (1989); I. M. Lichtzier and S. D. Odintsov,Europhys. Lett.,7, 95 (1988).

    Google Scholar 

  28. I. K. Buchbinder, I. L. Shapiro, and E. G. Yagunov,Mod. Phys. Lett. A,5, 1599 (1990).

    Google Scholar 

  29. E. S. Fradkin and G. A. Vilkovisky,Phys. Lett. B,73, 209 (1978).

    Google Scholar 

  30. F. Englert, C. Truffin, and R. Gastmans,Nucl. Phys. B,117, 407 (1976).

    Google Scholar 

  31. I. L. Shapiro and K. E. Osetrin, “Asymptotic freedom in the theory of a scalar field withR 2 quantum fravity,” Preprint [in Russian], Tomsk Scientific Center, Siberian Branch, USSR Academy of Sciences (1991).

  32. T. P. Cheng, E. Eichten, and L. F. Li,Phys. Rev. D,9, 2259 (1974).

    Google Scholar 

  33. I. L. Shapiro, Yu. Yu. Vol'fengaut, and E. G. Yagunov,Yad. Fiz.,51, 1791 (1990).

    Google Scholar 

  34. I. L. Buchbinder, P. M. Lavrov, and S. D. Odintsov,Nucl. Phys. B,308, 191 (1988); S. D. Odintsov,Phys. Lett. B,215, 483 (1988).

    Google Scholar 

  35. P. M. Lavrov, S. D. Odintsov, and I. V. Tyutin,Yad. Fiz.,46, 1583 (1987);Mod. Phys. Lett. A,3, 1273 (1988).

    Google Scholar 

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Authors
  1. S. D. Odintsov
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  2. I. L. Shapiro
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Additional information

Tomsk State Pedagogical Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 3, pp. 469–480, March, 1992.

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Odintsov, S.D., Shapiro, I.L. Curvature phase transition inR 2 quantum gravity and induction of Einstein gravity. Theor Math Phys 90, 319–326 (1992). https://doi.org/10.1007/BF01036537

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  • DOI: https://doi.org/10.1007/BF01036537

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