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Prog. Theor. Phys. Vol. 108 No. 2 (2002) pp. 399-433

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Resummation and Higher Order Renormalization in 4D Quantum Gravity

Ken-ji Hamada*

Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan

(Received May 31, 2002)

Abstract:

Higher order renormalization in 4D quantum gravity is carried out using dimensional regularization with great care concerning the conformal-mode dependence. In this regularization, resummation can be automatically carried out without making an assumption like that of David, Distler and Kawai. In this paper we consider a model of 4D quantum gravity coupled to QED. Resummation inevitably implies a four-derivative quantum gravity. The renormalizability is directly checked up to O(er6) and O(tr2), where er and tr are the running coupling constants of QED and the traceless gravitational mode. There is no other running coupling constant in our model. The conformal mode is treated exactly, which means it is unrenormalized. It is found that Hathrell's results are included in our results. As a by-product, it is found that a higher-order gravitational correction to the beta function of QED is negative. An advantage of our model is that in the very high-energy regime, it closely resembles exactly solvable 2D quantum gravity. Thus, we can study physical states of 4D quantum gravity in this regime in parallel to those of 2D quantum gravity, which can be described with diffeomorphism invariant composite fields.


URL : http://ptp.ipap.jp/link?PTP/108/399/
DOI : 10.1143/PTP.108.399


*E-mail: hamada@post.kek.jp

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References:

  1. B. DeWitt, in Relativity, Groups and Topology, ed. B. DeWitt and C. DeWitt (Gordon and Breach, New York, 1964); Phys. Rev. 160 (1967), 1113[APS]; ibid. 162 (1967), 1195[APS]; ibid. 162 (1967), 1239[APS].
  2. G. 't Hooft and M. Veltmann, Ann. Inst. Henri Poincare XX (1974), 69.
    M. Veltmann, in Methods in Field Theory, Les Houches 1975.
  3. S. Weinberg, in General Relativity, an Einstein Centenary Survey, ed. S. Hawking and W. Israel (Cambridge Univ. Press, Cambridge, 1979).
  4. R. Utiyama and B. DeWitt, J. Math. Phys. 3 (1962), 608[AIP Scitation].
  5. S. Deser, Proceedings of the Coference on Gauge Theories and Modern Field Theories, ed. R. Arnowitt and P. Nath (MIT Press, Cambridge, 1975).
    S. Weinberg, Proceedings of the XVIIth International Conference on High Energy Physics, ed. J. R. Smith (Rutherford Laboratory, Chilton, Didcot, 1974).
  6. K. Stelle, Phys. Rev. D 16 (1977), 953[APS]; Gen. Relat. Gravit. J. 9 (1978), 353.
    A. Salam and J. Strathdee, Phys. Rev. D 18 (1978), 4480[APS].
  7. J. Julve and M. Tonin, Nuovo Cim. 46B (1978), 137.
  8. E. Tomboulis, Phys. Lett. 70B (1977), 361; ibid. 97B (1980), 77.
    B. Hasslacher and E. Mottola, Phys. Lett. 99B (1981), 221.
  9. E. Fradkin and A. Tseytlin, Nucl. Phys. B 201 (1982), 469[CrossRef]; Phys. Lett. 104B (1981), 377.
  10. E. Elizalde, S. Odintsov and A. Romeo, Phys. Rev. D 51 (1995), 1680[APS]; ibid. 51 (1995), 4250[APS].
  11. M. Kaku, Nucl. Phys. B 203 (1982), 285[CrossRef].
    D. Boulware, G. Horowitz and A. Strominger, Phys. Rev. Lett. 50 (1983), 1726[APS].
    E. Tomboulis, Phys. Rev. Lett. 52 (1984), 1173[APS]; Phys. Lett. B 389 (1996), 225[CrossRef].
  12. R. Riegert, Phys. Lett. 134B (1984), 56.
  13. E. Fradkin and A. Tseytlin, Phys. Lett. 134B (1984), 187.
  14. I. Antoniadis and E. Mottola, Phys. Rev. D 45 (1992), 2013[APS].
    S. Odintsov, Z. Phys. C 54 (1992), 531.
  15. I. Antoniadis, P. Mazur and E. Mottola, Nucl. Phys. B 388 (1992), 627[CrossRef].
  16. I. Antoniadis, P. Mazur and E. Mottola, Phys. Lett. B 323 (1994), 284[CrossRef]; ibid. 394 (1997), 49[CrossRef].
    I. Antoniadis and S. Odintsov, Phys. Lett. B 343 (1995), 76[CrossRef].
  17. K. Hamada and F. Sugino, Nucl. Phys. B 553 (1999), 283, [CrossRef] hep-th/9810095[e-print arXiv].
  18. K. Hamada, Prog. Theor. Phys. 103 (2000), 1237, [IPAP] hep-th/9912098[e-print arXiv].
  19. K. Hamada, Prog. Theor. Phys. 105 (2001), 673, [IPAP] hep-th/0012053[e-print arXiv].
  20. T. Lee and G. Wick, Nucl. Phys. B 9 (1969), 209[CrossRef]; Phys. Rev. D 2 (1970), 1033[APS]; ibid. 3 (1971), 1046[APS].
    R. Cutkosky, P. Landshoff, D. Olive and J. Polkinghorne, Nucl. Phys. B 12 (1969), 281[CrossRef].
    N. Nakanishi, Prog. Theor. Phys. Suppl. No. 51 (1972), 1[IPAP].
    D. Boulware and D. Gross, Nucl. Phys. B 233 (1984), 1[CrossRef].
  21. A. Polyakov, Phys. Lett. 103B (1981), 207; Mod. Phys. Lett. A 2 (1987), 893.
  22. V. Knizhnik, A. Polyakov and A. Zamolodchikov, Mod. Phys. Lett. A 3 (1988), 819.
  23. J. Distler and H. Kawai, Nucl. Phys. B 321 (1989), 509[CrossRef].
    F. David, Mod. Phys. Lett. A 3 (1988), 1651.
  24. N. Seiberg, Prog. Theor. Phys. Suppl. No. 102 (1990), 319[IPAP].
    J. Polchinski, Proc. of String 1990, Texas A& M, March 1990; Nucl. Phys. B 346 (1990), 253[CrossRef].
    K. Hamada, Phys. Lett. B 324 (1994), 141[CrossRef]; Nucl. Phys. B 413 (1994), 278[CrossRef].
  25. K. Hamada, Phys. Lett. B 300 (1993), 322[CrossRef].
    K. Hamada and A. Tsuchiya, Int. J. Mod. Phys. A 8 (1993), 4897.
  26. P. Bouwknegt, J. McCarthy and K. Pilch, Commun. Math. Phys. 145 (1992), 541[CrossRef].
  27. H. Kawai and M. Ninomiya, Nucl. Phys. B 336 (1990), 115[CrossRef].
    H. Kawai, Y. Kitazawa and M. Ninomiya, Nucl. Phys. B 393 (1993), 280[CrossRef]; ibid. 404 (1993), 684[CrossRef].
    T. Aida, Y. Kitazawa, H. Kawai and M. Ninomiya, Nucl. Phys. B 427 (1994), 158[CrossRef].
    T. Aida, Y. Kitazawa, J. Nishimura and A. Tsuchiya, Nucl. Phys. B 444 (1995), 353[CrossRef].
    H. Kawai, Y. Kitazawa and M. Ninomiya, Nucl. Phys. B 467 (1996), 313[CrossRef].
    T. Aida and Y. Kitazawa, Nucl. Phys. B 491 (1997), 427[CrossRef].
  28. S. Hathrell, Ann. of Phys. 139 (1982), 136[CrossRef].
  29. S. Hathrell, Ann. of Phys. 142 (1982), 34[CrossRef].
  30. M. Freeman, Ann. of Phys. 153 (1984), 339[CrossRef].
  31. J. Wess and B. Zumino, Phys. Lett. 37B (1971), 95.
  32. L. Bonora, P. Cotta-Ramusino and C. Reina, Phys. Lett. B 126 (1983), 305[CrossRef].
  33. D. Capper and M. Duff, Nuovo Cim. 23A (1974), 173.
  34. S. Deser, M. Duff and C. Isham, Nucl. Phys. B 111 (1976), 45[CrossRef].
  35. M. Duff, Nucl. Phys. B 125 (1977), 334[CrossRef].
    Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994), 1387, [IoP STACKS] hep-th/9308075[e-print arXiv], and references therein.
  36. K. Fujikawa, Phys. Rev. D 23 (1981), 2262[APS]; Phys. Rev. Lett. 44 (1980), 1733[APS].
  37. S. Deser and A. Schwimmer, Phys. Lett. B 309 (1993), 279, [CrossRef] hep-th/9302047[e-print arXiv].
  38. I. Drummond and S. Hathrell, Phys. Rev. D 21 (1980), 958[APS].
  39. L. Abbott, Nucl. Phys. B 185 (1981), 189[CrossRef].
  40. E. DeRafael and J. Rosner, Ann. of Phys. 82 (1974), 369[CrossRef].
  41. K. Hamada, Mod. Phys. Lett. A 16 (2001), 803, hep-th/0101100[e-print arXiv].
  42. D. Weingarten, Phys. Lett. B 90 (1980), 285[CrossRef]; Nucl. Phys. B 210 [FS6] (1982), 229.
    V. Kazakov, Phys. Lett. 150B (1985), 282.
    F. David, Nucl. Phys. B 257 (1985), 45[CrossRef].
    J. Ambjørn, B. Durhuus and J. Fröhlich, Nucl. Phys. B 257 (1985), 433[CrossRef].
    D. Boulatov, V. Kazakov, I. Kostov and A. Migdal, Nucl. Phys. B 275 (1986), 641[CrossRef].
  43. E. Brezin and V. Kazakov, Phys. Lett. B 236 (1990), 144[CrossRef].
    M. Douglas and S. Shenker, Nucl. Phys. B 335 (1990), 635[CrossRef].
    D. Gross and A. Migdal, Phys. Rev. Lett. 64 (1990), 127[APS].
  44. J. Ambjørn, B. Durhuus and T. Jonsson, Quantum Geometry (Cambridge Univ. Press, Cambridge, 1997).
  45. M. Agishtein and A. Migdal, Nucl. Phys. B 385 (1992), 395[CrossRef].
    J. Ambjørn and J. Jurkiewicz, Phys. Lett. B 278 (1992), 42[CrossRef].
    S. Catterall, J. Kogut and R. Renken, Phys. Lett. B 328 (1994), 277[CrossRef].
  46. S. Bilke, Z. Burda, A. Krzywicki, B. Petersson, J. Tabaczek and G. Thorleifsson, Phys. Lett. B 418 (1998), 266[CrossRef]; ibid. 432 (1998), 279[CrossRef].
  47. H. Egawa, A. Fujitu, S. Horata, N. Tsuda and T. Yukawa, Nucl. Phys. B (Proc. Suppl.) 73 (1999), 795, [CrossRef] hep-lat/9809028[e-print arXiv].
    S. Horata, H. Egawa, N. Tsuda and T. Yukawa, Nucl. Phys. B (Proc. Suppl.) 83 (2000), 751, [Elsevier] hep-lat/9908048[e-print arXiv]; Prog. Theor. Phys. 106 (2001), 1037, [IPAP] hep-lat/0004021[e-print arXiv].
    S. Horata, H. Egawa and T. Yukawa, Nucl. Phys. B (Proc. Suppl.) 94 (2001), 701, [CrossRef] hep-lat/0010050[e-print arXiv].
  48. S. Horata, H. Egawa and T. Yukawa, Nucl. Phys. B (Proc. Suppl.) 106 (2002), 971, [Elsevier] hep-lat/0110042[e-print arXiv].
  49. H. Hagura, Nucl. Phys. B (Proc. Suppl.) 94 (2001), 704[CrossRef].

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