Skip to main content
SpringerLink
Log in

Running couplings in quantum theory of gravity coupled with gauge fields

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

In this paper we study the coupled system of non-abelian gauge fields with higher-derivative gravity. Charge renormalization is investigated in this coupled system. It is found that the leading term in the gauge coupling beta function comes due to interaction of gauge fields with gravitons. This is shown to be a universal quantity in the sense that it doesn’t depend on the gauge coupling and the gauge group, but may depend on the other couplings of the action (gravitational and matter). The coupled system is studied at one-loop. It is found that the leading term of gauge beta function is zero at one-loop in four dimensions. The effect of gauge fields on the running of gravitational couplings is investigated. The coupled system of gauge field with higher-derivative gravity is shown to satisfy unitarity when quantum corrections are taken in to account. Moreover, it is found that Newton constant goes to zero at short distances. In this renormalizable and unitary theory of gauge field coupled with higher-derivative gravity, the leading term of the gauge beta function, found to be universal for all gauge groups, is further studied in more detail by isolating it in the context of abelian gauge theories coupled with gravity in four dimensions. Using self-duality of abelian gauge theories in four dimensions, this term of the gauge beta function is shown to be zero to all loops. This is found to be independent of the gravity action, regularization scheme and gauge fixing condition. An explicit one-loop computation for arbitrary gravity action further demonstrates the vanishing of this term in the gauge beta function in four dimensions, independent of the regularization scheme and gauge fixing condition. Consequences of this are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Elias-Miro et al., Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].

    Article  ADS  Google Scholar 

  2. G. Degrassi et al., Higgs mass and vacuum stability in the standard model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].

    Article  ADS  Google Scholar 

  3. I. Masina, Higgs boson and top quark masses as tests of electroweak vacuum stability, Phys. Rev. D 87 (2013) 053001 [arXiv:1209.0393] [INSPIRE].

    ADS  Google Scholar 

  4. H. Georgi and S.L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].

    Article  ADS  Google Scholar 

  5. H. Georgi, H.R. Quinn and S. Weinberg, Hierarchy of interactions in unified gauge theories, Phys. Rev. Lett. 33 (1974) 451 [INSPIRE].

    Article  ADS  Google Scholar 

  6. S. Dimopoulos, S. Raby and F. Wilczek, Supersymmetry and the scale of unification, Phys. Rev. D 24 (1981) 1681 [INSPIRE].

    ADS  Google Scholar 

  7. J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. J.F. Donoghue, Leading quantum correction to the Newtonian potential, Phys. Rev. Lett. 72 (1994) 2996 [gr-qc/9310024] [INSPIRE].

    Article  ADS  Google Scholar 

  9. J.F. Donoghue, General relativity as an effective field theory: the leading quantum corrections, Phys. Rev. D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].

    ADS  Google Scholar 

  10. J.F. Donoghue, Introduction to the effective field theory description of gravity, gr-qc/9512024 [INSPIRE].

  11. G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20 (1974) 69 [INSPIRE].

  12. S. Deser and P. van Nieuwenhuizen, Nonrenormalizability of the quantized Einstein-Maxwell system, Phys. Rev. Lett. 32 (1974) 245 [INSPIRE].

    Article  ADS  Google Scholar 

  13. S. Deser and P. van Nieuwenhuizen, Nonrenormalizability of quantized fermion-gravitation interactions, Lett. Nuovo Cim. 11S2 (1974) 218 [INSPIRE].

    Google Scholar 

  14. S. Deser and P. van Nieuwenhuizen, Nonrenormalizability of the quantized Dirac-Einstein system, Phys. Rev. D 10 (1974) 411 [INSPIRE].

    ADS  Google Scholar 

  15. S. Deser, H.-S. Tsao and P. van Nieuwenhuizen, Nonrenormalizability of Einstein Yang-Mills interactions at the one loop level, Phys. Lett. B 50 (1974) 491 [INSPIRE].

    Article  ADS  Google Scholar 

  16. S. Deser and P. van Nieuwenhuizen, One loop divergences of quantized Einstein-Maxwell fields, Phys. Rev. D 10 (1974) 401 [INSPIRE].

    ADS  Google Scholar 

  17. S. Deser, H.-S. Tsao and P. van Nieuwenhuizen, One loop divergences of the Einstein Yang-Mills system, Phys. Rev. D 10 (1974) 3337 [INSPIRE].

    ADS  Google Scholar 

  18. G. ’t Hooft, Dimensional regularization and the renormalization group, Nucl. Phys. B 61 (1973) 455 [INSPIRE].

  19. S.P. Robinson and F. Wilczek, Gravitational correction to running of gauge couplings, Phys. Rev. Lett. 96 (2006) 231601 [hep-th/0509050] [INSPIRE].

    Article  ADS  Google Scholar 

  20. A.R. Pietrykowski, Gauge dependence of gravitational correction to running of gauge couplings, Phys. Rev. Lett. 98 (2007) 061801 [hep-th/0606208] [INSPIRE].

    Article  ADS  Google Scholar 

  21. D.J. Toms, Quantum gravity and charge renormalization, Phys. Rev. D 76 (2007) 045015 [arXiv:0708.2990] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  22. G.A. Vilkovisky, The unique effective action in quantum field theory, Nucl. Phys. B 234 (1984) 125 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. D. Ebert, J. Plefka and A. Rodigast, Absence of gravitational contributions to the running Yang-Mills coupling, Phys. Lett. B 660 (2008) 579 [arXiv:0710.1002] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. Y. Tang and Y.-L. Wu, Gravitational contributions to the running of gauge couplings, Commun. Theor. Phys. 54 (2010) 1040 [arXiv:0807.0331] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  25. D.J. Toms, Cosmological constant and quantum gravitational corrections to the running fine structure constant, Phys. Rev. Lett. 101 (2008) 131301 [arXiv:0809.3897] [INSPIRE].

    Article  ADS  Google Scholar 

  26. D.J. Toms, Quantum gravity, gauge coupling constants and the cosmological constant, Phys. Rev. D 80 (2009) 064040 [arXiv:0908.3100] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. D.J. Toms, Quantum gravitational contributions to quantum electrodynamics, Nature 468 (2010) 56 [arXiv:1010.0793] [INSPIRE].

    Article  ADS  Google Scholar 

  28. D.J. Toms, Quadratic divergences and quantum gravitational contributions to gauge coupling constants, Phys. Rev. D 84 (2011) 084016 [INSPIRE].

    ADS  Google Scholar 

  29. J.-E. Daum, U. Harst and M. Reuter, Running gauge coupling in asymptotically safe quantum gravity, JHEP 01 (2010) 084 [arXiv:0910.4938] [INSPIRE].

    Article  ADS  Google Scholar 

  30. S. Folkerts, D.F. Litim and J.M. Pawlowski, Asymptotic freedom of Yang-Mills theory with gravity, Phys. Lett. B 709 (2012) 234 [arXiv:1101.5552] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in S.W. Hawking and W. Israel, General relativity (1979), pp. 790–831 [INSPIRE].

  32. M. Niedermaier and M. Reuter, The asymptotic safety scenario in quantum gravity, Living Rev. Rel. 9 (2006) 5 [INSPIRE].

    Google Scholar 

  33. M. Niedermaier, The asymptotic safety scenario in quantum gravity: an introduction, Class. Quant. Grav. 24 (2007) R171 [gr-qc/0610018] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. R. Percacci, Asymptotic safety, in D. Oriti ed., Approaches to quantum gravity: towards a new understanding of space, time and matter, Cambridge University Press, Cambridge U.K. (2007), pp. 111–128 [arXiv:0709.3851] [INSPIRE].

  35. D.F. Litim, Fixed points of quantum gravity and the renormalisation group, arXiv:0810.3675 [INSPIRE].

  36. M.M. Anber, J.F. Donoghue and M. El-Houssieny, Running couplings and operator mixing in the gravitational corrections to coupling constants, Phys. Rev. D 83 (2011) 124003 [arXiv:1011.3229] [INSPIRE].

    ADS  Google Scholar 

  37. K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  38. G. Narain and R. Anishetty, Short distance freedom of quantum gravity, Phys. Lett. B 711 (2012) 128 [arXiv:1109.3981] [INSPIRE].

    Article  ADS  Google Scholar 

  39. G. Narain and R. Anishetty, Unitary and renormalizable theory of higher derivative gravity, J. Phys. Conf. Ser. 405 (2012) 012024 [arXiv:1210.0513] [INSPIRE].

    Article  ADS  Google Scholar 

  40. E. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. T. Moriya and K. Yamagishi, Comment on renormalization of higher derivative quantum gravity: a coupling with the Maxwell field, Phys. Rev. D 22 (1980) 2561 [INSPIRE].

    ADS  Google Scholar 

  42. G. Narain and R. Anishetty, Charge renormalization due to graviton loops, JHEP 07 (2013) 106 [arXiv:1211.5040] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  43. R. Utiyama and B.S. DeWitt, Renormalization of a classical gravitational field interacting with quantized matter fields, J. Math. Phys. 3 (1962) 608 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. M.H. Goroff and A. Sagnotti, Quantum gravity at two loops, Phys. Lett. B 160 (1985) 81 [INSPIRE].

    Article  ADS  Google Scholar 

  45. M.H. Goroff and A. Sagnotti, The ultraviolet behavior of Einstein gravity, Nucl. Phys. B 266 (1986) 709 [INSPIRE].

    Article  ADS  Google Scholar 

  46. A.E.M. van de Ven, Two loop quantum gravity, Nucl. Phys. B 378 (1992) 309 [INSPIRE].

    ADS  Google Scholar 

  47. J. Julve and M. Tonin, Quantum gravity with higher derivative terms, Nuovo Cim. B 46 (1978) 137 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. A. Salam and J.A. Strathdee, Remarks on high-energy stability and renormalizability of gravity theory, Phys. Rev. D 18 (1978) 4480 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  49. B.S. DeWitt, Quantum theory of gravity. II. The manifestly covariant theory, Phys. Rev. 162 (1967) 1195 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  50. B.S. DeWitt, Quantum theory of gravity. III. Applications of the covariant theory, Phys. Rev. 162 (1967) 1239 [INSPIRE].

    Article  ADS  Google Scholar 

  51. B.S. DeWitt, A gauge invariant effective action, in C.J. Isham, R. Penrose and D.W. Sciama eds., Proceedings of Oxford 1980. Quantum gravity 2, Clarendon Press, Oxford U.K. (1981), pp. 449–487 [NSF-ITP-80-031] [INSPIRE].

  52. L.F. Abbott, The background field method beyond one loop, Nucl. Phys. B 185 (1981) 189 [INSPIRE].

    Article  ADS  Google Scholar 

  53. E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Phys. Lett. B 104 (1981) 377 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. L.D. Faddeev and V.N. Popov, Feynman diagrams for the Yang-Mills field, Phys. Lett. B 25 (1967) 29 [INSPIRE].

    Article  ADS  Google Scholar 

  55. R.E. Kallosh, Modified Feynman rules in supergravity, Nucl. Phys. B 141 (1978) 141 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. N.K. Nielsen, Ghost counting in supergravity, Nucl. Phys. B 140 (1978) 499 [INSPIRE].

    Article  ADS  Google Scholar 

  57. I.L. Buchbinder, S.D. Odintsov and I.L. Shapiro, Effective action in quantum gravity, IOP Publishing, Bristol U.K. (1992) [INSPIRE].

    Google Scholar 

  58. E. Elizalde, S.D. Odintsov and A. Romeo, Improved effective potential in curved space-time and quantum matter, higher derivative gravity theory, Phys. Rev. D 51 (1995) 1680 [hep-th/9410113] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  59. E. Elizalde, C.O. Lousto, S.D. Odintsov and A. Romeo, GUTs in curved space-time: running gravitational constants, Newtonian potential and the quantum corrected gravitational equations, Phys. Rev. D 52 (1995) 2202 [hep-th/9504014] [INSPIRE].

    ADS  Google Scholar 

  60. E. Elizalde, S.D. Odintsov and A. Romeo, Renormalization group properties of higher derivative quantum gravity with matter in 4 − ε dimensions, Nucl. Phys. B 462 (1996) 315 [hep-th/9502131] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. I.G. Avramidi, Heat kernel and quantum gravity, Lect. Notes Phys. M 64 (2000) 1 [INSPIRE].

    MathSciNet  Google Scholar 

  62. E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space, II. The standard model and beyond, JHEP 06 (2003) 004 [hep-ph/0303124] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. G. de Berredo-Peixoto and I.L. Shapiro, Higher derivative quantum gravity with Gauss-Bonnet term, Phys. Rev. D 71 (2005) 064005 [hep-th/0412249] [INSPIRE].

    ADS  Google Scholar 

  64. A. Codello and R. Percacci, Fixed points of higher derivative gravity, Phys. Rev. Lett. 97 (2006) 221301 [hep-th/0607128] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  65. D. Benedetti, P.F. Machado and F. Saueressig, Asymptotic safety in higher-derivative gravity, Mod. Phys. Lett. A 24 (2009) 2233 [arXiv:0901.2984] [INSPIRE].

    Article  ADS  Google Scholar 

  66. M.R. Niedermaier, Gravitational fixed points from perturbation theory, Phys. Rev. Lett. 103 (2009) 101303 [INSPIRE].

    Article  ADS  Google Scholar 

  67. C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [INSPIRE].

    Article  ADS  Google Scholar 

  68. R. Savit, Topological excitations in U(1) invariant theories, Phys. Rev. Lett. 39 (1977) 55 [INSPIRE].

    Article  ADS  Google Scholar 

  69. M.E. Peskin, Mandelstam-’t Hooft duality in Abelian lattice models, Annals Phys. 113 (1978) 122 [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, Taramani, Chennai, 600113, India

    Gaurav Narain & Ramesh Anishetty

Authors
  1. Gaurav Narain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramesh Anishetty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gaurav Narain.

Additional information

ArXiv ePrint: 1309.0473

Rights and permissions

Reprints and permissions

About this article

Cite this article

Narain, G., Anishetty, R. Running couplings in quantum theory of gravity coupled with gauge fields. J. High Energ. Phys. 2013, 203 (2013). https://doi.org/10.1007/JHEP10(2013)203

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2013)203

Keywords

Search

Navigation