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Running gauge coupling in asymptotically safe quantum gravity

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Abstract

We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.

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References

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

    Article  ADS  Google Scholar 

  2. S.P. Robinson, Two quantum effects in the theory of gravitation, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge U.S.A. (2005).

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

    Article  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  5. 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] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  6. Y. Tang and Y.-L. Wu, Gravitational contributions to the running of gauge couplings, arXiv:0807.0331 [SPIRES].

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

    Article  ADS  Google Scholar 

  8. S. Weinberg, General relativity, an Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979).

    Google Scholar 

  9. S. Weinberg, Living with infinities, arXiv:0903.0568 [SPIRES].

  10. S. Weinberg, Effective field theory, past and future, arXiv:0908.1964 [SPIRES].

  11. M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  12. D. Dou and R. Percacci, The running gravitational couplings, Class. Quant. Grav. 15 (1998) 3449 [hep-th/9707239] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity, Phys. Rev. D 65 (2002) 025013 [hep-th/0108040] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  14. M. Reuter and F. Saueressig, Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation, Phys. Rev. D 65 (2002) 065016 [hep-th/0110054] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. O. Lauscher and M. Reuter, Flow equation of Quantum Einstein Gravity in a higherderivative truncation, Phys. Rev. D 66 (2002) 025026 [hep-th/0205062] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. O. Lauscher and M. Reuter, Is Quantum Einstein Gravity nonperturbatively renormalizable?, Class. Quant. Grav. 19 (2002) 483 [hep-th/0110021] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. O. Lauscher and M. Reuter, Towards nonperturbative renormalizability of Quantum Einstein Gravity, Int. J. Mod. Phys. A 17 (2002) 993 [hep-th/0112089] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  18. W. Souma, Non-trivial ultraviolet fixed point in quantum gravity, Prog. Theor. Phys. 102 (1999) 181 [hep-th/9907027] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. M. Reuter and F. Saueressig, A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior, Phys. Rev. D 66 (2002) 125001 [hep-th/0206145] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. M. Reuter and F. Saueressig, Nonlocal quantum gravity and the size of the universe, Fortschr. Phys. 52 (2004) 650 [hep-th/0311056] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  21. A. Bonanno and M. Reuter, Proper time flow equation for gravity, JHEP 02 (2005) 035 [hep-th/0410191] [SPIRES]

    Article  MathSciNet  ADS  Google Scholar 

  22. M. Reuter and F. Saueressig, Functional renormalization group equations, asymptotic safety and Quantum Einstein Gravity, arXiv:0708.1317 [SPIRES].

  23. O. Lauscher and M. Reuter, Quantum gravity, B. Fauser, J. Tolksdorf and E. Zeidler eds., Birkhäuser, Basel (2007) [hep-th/0511260] [SPIRES].

    Google Scholar 

  24. O. Lauscher and M. Reuter, Approaches to fundamental physics, I.-O. Stamatescu and E. Seiler eds., Springer, Berlin (2007).

    Google Scholar 

  25. R. Percacci and D. Perini, Constraints on matter from asymptotic safety, Phys. Rev. D 67 (2003) 081503 [hep-th/0207033] [SPIRES].

    ADS  Google Scholar 

  26. R. Percacci and D. Perini, Asymptotic safety of gravity coupled to matter, Phys. Rev. D 68 (2003) 044018 [hep-th/0304222] [SPIRES].

    ADS  Google Scholar 

  27. R. Percacci and D. Perini, Should we expect a fixed point for Newton’s constant?, Class. Quant. Grav. 21 (2004) 5035 [hep-th/0401071] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  29. A. Codello, R. Percacci and C. Rahmede, Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation, Annals Phys. 324 (2009) 414 [arXiv:0805.2909] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. O. Zanusso, L. Zambelli, G.P. Vacca and R. Percacci, Gravitational corrections to Yukawa systems, arXiv:0904.0938 [SPIRES].

  31. D.F. Litim, Fixed points of quantum gravity, Phys. Rev. Lett. 92 (2004) 201301 [hep-th/0312114] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. D. Litim, On fixed points of quantum gravity, AIP Conf. Proc. 841 (2006) 322 [hep-th/0606044] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. P. Fischer and D.F. Litim, Fixed points of quantum gravity in extra dimensions, Phys. Lett. B 638 (2006) 497 [hep-th/0602203] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  34. P. Fischer and D. Litim, Fixed points of quantum gravity in higher dimensions, AIP Conf. Proc. 861 (2006) 336 [hep-th/0606135] [SPIRES].

    Article  ADS  Google Scholar 

  35. P.F. Machado and F. Saueressig, On the renormalization group flow of f(R)-gravity, Phys. Rev. D 77 (2008) 124045 [arXiv:0712.0445] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  37. D. Benedetti, P.F. Machado and F. Saueressig, Taming perturbative divergences in asymptotically safe gravity, Nucl. Phys. B 824 (2010) 168 [arXiv:0902.4630] [SPIRES].

    Article  Google Scholar 

  38. A. Eichhorn, H. Gies and M.M. Scherer, Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity, Phys. Rev. D 80 (2009) 104003 [arXiv:0907.1828] [SPIRES].

    Google Scholar 

  39. O. Lauscher and M. Reuter, Fractal spacetime structure in asymptotically safe gravity, JHEP 10 (2005) 050 [hep-th/0508202] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  40. M. Reuter and J.-M. Schwindt, A minimal length from the cutoff modes in asymptotically safe quantum gravity, JHEP 01 (2006) 070 [hep-th/0511021] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. M. Reuter and J.-M. Schwindt, Scale-dependent metric and causal structures in Quantum Einstein Gravity, JHEP 01 (2007) 049 [hep-th/0611294] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. M. Reuter and H. Weyer, Background independence and asymptotic safety in conformally reduced gravity, Phys. Rev. D 79 (2009) 105005 [arXiv:0801.3287] [SPIRES].

    ADS  Google Scholar 

  43. M. Reuter and H. Weyer, The role of background independence for asymptotic safety in Quantum Einstein Gravity, Gen. Rel. Grav. 41 (2009) 983 [arXiv:0903.2971] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. M. Reuter and H. Weyer, Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of diffeomorphism invariance, Phys. Rev. D 80 (2009) 025001 [arXiv:0804.1475] [SPIRES].

    ADS  Google Scholar 

  45. P.F. Machado and R. Percacci, Conformally reduced quantum gravity revisited, Phys. Rev. D 80 (2009) 024020 [arXiv:0904.2510] [SPIRES].

    ADS  Google Scholar 

  46. E. Manrique and M. Reuter, Bare action and regularized functional integral of asymptotically safe quantum gravity, Phys. Rev. D 79 (2009) 025008 [arXiv:0811.3888] [SPIRES].

    ADS  Google Scholar 

  47. E. Manrique and M. Reuter, Bare vs. effective fixed point action in asymptotic safety: the reconstruction problem, arXiv:0905.4220 [SPIRES].

  48. E. Manrique and M. Reuter, Bimetric truncations for Quantum Einstein Gravity and ssymptotic safety, arXiv:0907.2617 [SPIRES].

  49. J.-E. Daum and M. Reuter, Effective potential of the conformal factor: gravitational average action and dynamical triangulations, Adv. Sci. Lett. 2 (2009) 255 [arXiv:0806.3907] [SPIRES].

    Google Scholar 

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

    Article  Google Scholar 

  51. P. Forgács and M. Niedermaier, A fixed point for truncated Quantum Einstein Gravity, hep-th/0207028 [SPIRES].

  52. M. Niedermaier, Renormalization and asymptotic safety in truncated Quantum Einstein Gravity, JHEP 12 (2002) 066 [hep-th/0207143] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  53. M. Niedermaier, Dimensionally reduced gravity theories are asymptotically safe, Nucl. Phys. B 673 (2003) 131 [hep-th/0304117] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  56. R. Percacci, Asymptotic safety, arXiv:0709.3851 [SPIRES].

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

    ADS  Google Scholar 

  58. M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181 [SPIRES].

    Article  ADS  Google Scholar 

  59. M. Reuter and C. Wetterich, Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 [SPIRES].

    Article  ADS  Google Scholar 

  60. M. Reuter and C. Wetterich, Average action for the Higgs model with Abelian gauge symmetry, Nucl. Phys. B 391 (1993) 147 [SPIRES].

    Article  ADS  Google Scholar 

  61. M. Reuter and C. Wetterich, Running gauge coupling in three-dimensions and the electroweak phase transition, Nucl. Phys. B 408 (1993) 91 [SPIRES].

    Article  ADS  Google Scholar 

  62. M. Reuter, Effective average action of Chern-Simons field theory, Phys. Rev. D 53 (1996) 4430.

    ADS  Google Scholar 

  63. M. Reuter, Renormalization of the topological charge in Yang-Mills theory, Mod. Phys. Lett. A 12 (1997) 2777 [hep-th/9604124] [SPIRES].

    ADS  Google Scholar 

  64. M. Reuter and C. Wetterich, Gluon condensation in nonperturbative flow equations, Phys. Rev. D 56 (1997) 7893 [hep-th/9708051] [SPIRES].

    ADS  Google Scholar 

  65. H. Gies, Renormalizability of gauge theories in extra dimensions, Phys. Rev. D 68 (2003) 085015 [hep-th/0305208] [SPIRES].

    ADS  Google Scholar 

  66. J. Berges, N. Tetradis and C. Wetterich, Non-perturbative renormalization flow in quantum field theory and statistical physics, Phys. Rept. 363 (2002) 223 [hep-ph/0005122] [SPIRES].

    MathSciNet  ADS  MATH  Google Scholar 

  67. C. Wetterich, Effective average action in statistical physics and quantum field theory, Int. J. Mod. Phys. A 16 (2001) 1951 [hep-ph/0101178] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  68. M. Reuter, Effective average actions and nonperturbative evolution equations, hep-th/9602012 [SPIRES].

  69. J.M. Pawlowski, Aspects of the functional renormalisation group, Annals Phys. 322 (2007) 2831 [hep-th/0512261] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  70. H. Gies, Introduction to the functional RG and applications to gauge theories, hep-ph/0611146 [SPIRES].

  71. D.F. Litim, Optimisation of the exact renormalisation group, Phys. Lett. B 486 (2000) 92 [hep-th/0005245] [SPIRES].

    ADS  Google Scholar 

  72. D.F. Litim, Optimised renormalisation group flows, Phys. Rev. D 64 (2001) 105007 [hep-th/0103195] [SPIRES].

    ADS  Google Scholar 

  73. D.F. Litim, Mind the gap, Int. J. Mod. Phys. A 16 (2001) 2081 [hep-th/0104221] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  74. A. Bonanno and M. Reuter, Renormalization group improved black hole spacetimes, Phys. Rev. D 62 (2000) 043008 [hep-th/0002196] [SPIRES].

    ADS  Google Scholar 

  75. A. Bonanno and M. Reuter, Spacetime structure of an evaporating black hole in quantum gravity, Phys. Rev. D 73 (2006) 083005 [hep-th/0602159] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  76. A. Bonanno and M. Reuter, Quantum gravity effects near the null black hole singularity, Phys. Rev. D 60 (1999) 084011 [gr-qc/9811026] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  77. M. Reuter and E. Tuiran, Quantum gravity effects in rotating black holes, in Proceedings of the Eleventh Marcel Grossmann Meeting, H. Kleinert, R. Jantzen and R. Ruffini eds., World Scientific, Singapore (2007) [hep-th/0612037] [SPIRES].

    Google Scholar 

  78. A. Bonanno and M. Reuter, Cosmology of the Planck Era from a renormalization group for quantum gravity, Phys. Rev. D 65 (2002) 043508 [hep-th/0106133] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  79. M. Reuter and F. Saueressig, From big bang to asymptotic de Sitter: complete cosmologies in a quantum gravity framework, JCAP 09 (2005) 012 [hep-th/0507167] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  80. A. Bonanno and M. Reuter, Cosmology with self-adjusting vacuum energy density from a renormalization group fixed point, Phys. Lett. B 527 (2002) 9 [astro-ph/0106468] [SPIRES].

    ADS  Google Scholar 

  81. A. Bonanno and M. Reuter, Cosmological perturbations in renormalization group derived cosmologies, Int. J. Mod. Phys. D 13 (2004) 107 [astro-ph/0210472] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  82. E. Bentivegna, A. Bonanno and M. Reuter, Confronting the IR fixed point cosmology with high redshift supernova data, JCAP 01 (2004) 001 [astro-ph/0303150] [SPIRES].

    ADS  Google Scholar 

  83. A. Bonanno and M. Reuter, Entropy signature of the running cosmological constant, JCAP 08 (2007) 024 [arXiv:0706.0174] [SPIRES].

    ADS  Google Scholar 

  84. A. Bonanno and M. Reuter, Primordial entropy production and Λ-driven inflation from quantum Einstein gravity, J. Phys. Conf. Ser. 140 (2008) 012008 [arXiv:0803.2546] [SPIRES].

    Article  ADS  Google Scholar 

  85. A. Bonanno, G. Esposito and C. Rubano, A class of renormalization group invariant scalar field cosmologies, Gen. Rel. Grav. 35 (2003) 1899 [hep-th/0303154] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  86. A. Bonanno, G. Esposito and C. Rubano, Arnowitt-Deser-Misner gravity with variable G and Lambda and fixed point cosmologies from the renormalization group, Class. Quant. Grav. 21 (2004) 5005 [gr-qc/0403115] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  87. A. Bonanno, G. Esposito, C. Rubano and P. Scudellaro, The accelerated expansion of the universe as a crossover phenomenon, Class. Quant. Grav. 23 (2006) 3103 [astro-ph/0507670] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  88. A. Bonanno, G. Esposito, C. Rubano and P. Scudellaro, Noether symmetry approach in pure gravity with variable G and Λ, Class. Quant. Grav. 24 (2007) 1443 [gr-qc/0610012] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  89. M. Reuter and H. Weyer, Renormalization group improved gravitational actions: a Brans-Dicke approach, Phys. Rev. D 69 (2004) 104022 [hep-th/0311196] [SPIRES].

    ADS  Google Scholar 

  90. M. Reuter and H. Weyer, Running Newton constant, improved gravitational actions, and galaxy rotation curves, Phys. Rev. D 70 (2004) 124028 [hep-th/0410117] [SPIRES].

    ADS  Google Scholar 

  91. M. Reuter and H. Weyer, Quantum gravity at astrophysical distances?, JCAP 12 (2004) 001 [hep-th/0410119] [SPIRES].

    ADS  Google Scholar 

  92. F. Girelli, S. Liberati, R. Percacci and C. Rahmede, Modified dispersion relations from the renormalization group of gravity, Class. Quant. Grav. 24 (2007) 3995 [gr-qc/0607030] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  93. D.F. Litim and T. Plehn, Signatures of gravitational fixed points at the LHC, Phys. Rev. Lett. 100 (2008) 131301 [arXiv:0707.3983] [SPIRES].

    Article  ADS  Google Scholar 

  94. J. Moffat, Gravitational theory, galaxy rotation curves and cosmology without dark matter, JCAP 05 (2005) 003.

    MathSciNet  ADS  Google Scholar 

  95. J.R. Brownstein and J.W. Moffat, Galaxy rotation curves without non-baryonic dark matter, Astrophys. J. 636 (2006) 721 [astro-ph/0506370] [SPIRES].

    Article  ADS  Google Scholar 

  96. J.R. Brownstein and J.W. Moffat, Galaxy cluster masses without non-baryonic dark matter, Mon. Not. Roy. Astron. Soc. 367 (2006) 527 [astro-ph/0507222] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  98. L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B 13 (1982) 33 [SPIRES].

    MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  100. M.T. Grisaru, P.van Nieuwenhuizen and C.C. Wu, Background field method versus normal field theory in explicit examples: one loop divergences in S matrix and Green’s functions for Yang-Mills and gravitational fields, Phys. Rev. D 12 (1975) 3203 [SPIRES].

    ADS  Google Scholar 

  101. D.M. Capper, J.J. Dulwich and M. Ramon Medrano, The background field method for quantum gravity at two loops, Nucl. Phys. B 254 (1985) 737 [SPIRES].

    Article  ADS  Google Scholar 

  102. S.L. Adler, Einstein gravity as a symmetry breaking effect in quantum field theory, Rev. Mod. Phys. 54 (1982) 729 [Erratum ibid. 55 (1983) 837] [SPIRES].

    Article  ADS  Google Scholar 

  103. R. Jackiw, Gauge covariant conformal transformations, Phys. Rev. Lett. 41 (1978) 1635 [SPIRES].

    Article  ADS  Google Scholar 

  104. D.F. Litim and J.M. Pawlowski, Completeness and consistency of renormalisation group flows, Phys. Rev. D 66 (2002) 025030 [hep-th/0202188] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  105. C.A. Reuschle, Gravitational corrections to QED form factors, Diploma Thesis, Freiburg Germany (2009).

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  1. Institute of Physics, University of Mainz, Staudingerweg 7, D-55099, Mainz, Germany

    J.-E. Daum, U. Harst & M. Reuter

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  1. J.-E. Daum
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Daum, JE., Harst, U. & Reuter, M. Running gauge coupling in asymptotically safe quantum gravity. J. High Energ. Phys. 2010, 84 (2010). https://doi.org/10.1007/JHEP01(2010)084

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