Upper bound on the Abelian gauge coupling from asymptotic safety

Open Access
Regular Article - Theoretical Physics
  • 21 Downloads

Abstract

We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.

Keywords

Models of Quantum Gravity Renormalization Group Nonperturbative Effects 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A. Eichhorn and A. Held, Top mass from asymptotic safety, Phys. Lett. B 777 (2018) 217 [arXiv:1707.01107] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M. Baig, H. Fort, J.B. Kogut and S. Kim, The phases and triviality of scalar quantum electrodynamics, Phys. Rev. D 51 (1995) 5216 [hep-lat/9407017] [INSPIRE].
  3. [3]
    M. Baig, H. Fort, J.B. Kogut, S. Kim and D.K. Sinclair, On the logarithmic triviality of scalar quantum electrodynamics, Phys. Rev. D 48 (1993) R2385 [hep-lat/9305008] [INSPIRE].
  4. [4]
    S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General relativity, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K., (1980), pg. 790 [INSPIRE].
  5. [5]
    M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [INSPIRE].ADSMathSciNetGoogle Scholar
  6. [6]
    O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity, Phys. Rev. D 65 (2002) 025013 [hep-th/0108040] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    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] [INSPIRE].ADSMathSciNetGoogle Scholar
  8. [8]
    D.F. Litim, Fixed points of quantum gravity, Phys. Rev. Lett. 92 (2004) 201301 [hep-th/0312114] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    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] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    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].ADSCrossRefMATHGoogle Scholar
  11. [11]
    K. Falls, D.F. Litim, K. Nikolakopoulos and C. Rahmede, A bootstrap towards asymptotic safety, arXiv:1301.4191 [INSPIRE].
  12. [12]
    D. Becker and M. Reuter, En route to background independence: broken split-symmetry and how to restore it with bi-metric average actions, Annals Phys. 350 (2014) 225 [arXiv:1404.4537] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    H. Gies, B. Knorr, S. Lippoldt and F. Saueressig, Gravitational two-loop counterterm is asymptotically safe, Phys. Rev. Lett. 116 (2016) 211302 [arXiv:1601.01800] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    T. Denz, J.M. Pawlowski and M. Reichert, Towards apparent convergence in asymptotically safe quantum gravity, arXiv:1612.07315 [INSPIRE].
  15. [15]
    P. Donà, A. Eichhorn and R. Percacci, Matter matters in asymptotically safe quantum gravity, Phys. Rev. D 89 (2014) 084035 [arXiv:1311.2898] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A. Eichhorn and S. Lippoldt, Quantum gravity and Standard-Model-like fermions, Phys. Lett. B 767 (2017) 142 [arXiv:1611.05878] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J. Meibohm, J.M. Pawlowski and M. Reichert, Asymptotic safety of gravity-matter systems, Phys. Rev. D 93 (2016) 084035 [arXiv:1510.07018] [INSPIRE].ADSMathSciNetGoogle Scholar
  18. [18]
    P. Donà, A. Eichhorn, P. Labus and R. Percacci, Asymptotic safety in an interacting system of gravity and scalar matter, Phys. Rev. D 93 (2016) 044049 [Erratum ibid. D 93 (2016) 129904] [arXiv:1512.01589] [INSPIRE].
  19. [19]
    J. Biemans, A. Platania and F. Saueressig, Renormalization group fixed points of foliated gravity-matter systems, JHEP 05 (2017) 093 [arXiv:1702.06539] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    M. Niedermaier and M. Reuter, The asymptotic safety scenario in quantum gravity, Living Rev. Rel. 9 (2006) 5 [INSPIRE].CrossRefMATHGoogle Scholar
  21. [21]
    M. Niedermaier, The asymptotic safety scenario in quantum gravity: an introduction, Class. Quant. Grav. 24 (2007) R171 [gr-qc/0610018] [INSPIRE].
  22. [22]
    R. Percacci, Asymptotic safety, arXiv:0709.3851 [INSPIRE].
  23. [23]
    D.F. Litim, Fixed points of quantum gravity and the renormalisation group, arXiv:0810.3675 [INSPIRE].
  24. [24]
    D.F. Litim, Renormalisation group and the Planck scale, Phil. Trans. Roy. Soc. Lond. A 369 (2011) 2759 [arXiv:1102.4624] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    R. Percacci, A short introduction to asymptotic safety, arXiv:1110.6389 [INSPIRE].
  26. [26]
    M. Reuter and F. Saueressig, Quantum Einstein gravity, New J. Phys. 14 (2012) 055022 [arXiv:1202.2274] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    J. Ambjørn, A. Görlich, J. Jurkiewicz and R. Loll, Nonperturbative quantum gravity, Phys. Rept. 519 (2012) 127 [arXiv:1203.3591] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    M. Reuter and F. Saueressig, Asymptotic safety, fractals and cosmology, Lect. Notes Phys. 863 (2013) 185 [arXiv:1205.5431] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  29. [29]
    S. Nagy, Lectures on renormalization and asymptotic safety, Annals Phys. 350 (2014) 310 [arXiv:1211.4151] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    A. Ashtekar, M. Reuter and C. Rovelli, From general relativity to quantum gravity, arXiv:1408.4336 [INSPIRE].
  31. [31]
    A. Bonanno and F. Saueressig, Asymptotically safe cosmology — a status report, Comptes Rendus Physique 18 (2017) 254 [arXiv:1702.04137] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    A. Eichhorn, Status of the asymptotic safety paradigm for quantum gravity and matter, arXiv:1709.03696 [INSPIRE].
  33. [33]
    U. Harst and M. Reuter, QED coupled to QEG, JHEP 05 (2011) 119 [arXiv:1101.6007] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  34. [34]
    N. Christiansen and A. Eichhorn, An asymptotically safe solution to the U(1) triviality problem, Phys. Lett. B 770 (2017) 154 [arXiv:1702.07724] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    G. Narain and R. Percacci, Renormalization group flow in scalar-tensor theories. I, Class. Quant. Grav. 27 (2010) 075001 [arXiv:0911.0386] [INSPIRE].
  36. [36]
    O. Zanusso, L. Zambelli, G.P. Vacca and R. Percacci, Gravitational corrections to Yukawa systems, Phys. Lett. B 689 (2010) 90 [arXiv:0904.0938] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    J.-E. Daum, U. Harst and M. Reuter, Running gauge coupling in asymptotically safe quantum gravity, JHEP 01 (2010) 084 [arXiv:0910.4938] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  38. [38]
    G.P. Vacca and O. Zanusso, Asymptotic safety in Einstein gravity and scalar-fermion matter, Phys. Rev. Lett. 105 (2010) 231601 [arXiv:1009.1735] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    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].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    A. Eichhorn and H. Gies, Light fermions in quantum gravity, New J. Phys. 13 (2011) 125012 [arXiv:1104.5366] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A. Eichhorn, Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario, Phys. Rev. D 86 (2012) 105021 [arXiv:1204.0965] [INSPIRE].ADSGoogle Scholar
  42. [42]
    K.-Y. Oda and M. Yamada, Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity, Class. Quant. Grav. 33 (2016) 125011 [arXiv:1510.03734] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  43. [43]
    J. Meibohm and J.M. Pawlowski, Chiral fermions in asymptotically safe quantum gravity, Eur. Phys. J. C 76 (2016) 285 [arXiv:1601.04597] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    A. Eichhorn, A. Held and J.M. Pawlowski, Quantum-gravity effects on a Higgs-Yukawa model, Phys. Rev. D 94 (2016) 104027 [arXiv:1604.02041] [INSPIRE].ADSGoogle Scholar
  45. [45]
    A. Eichhorn and A. Held, Viability of quantum-gravity induced ultraviolet completions for matter, Phys. Rev. D 96 (2017) 086025 [arXiv:1705.02342] [INSPIRE].ADSGoogle Scholar
  46. [46]
    Y. Hamada and M. Yamada, Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system, JHEP 08 (2017) 070 [arXiv:1703.09033] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [arXiv:1710.05815] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    T.R. Morris, The exact renormalization group and approximate solutions, Int. J. Mod. Phys. A 9 (1994) 2411 [hep-ph/9308265] [INSPIRE].
  49. [49]
    J. Berges, N. Tetradis and C. Wetterich, Nonperturbative renormalization flow in quantum field theory and statistical physics, Phys. Rept. 363 (2002) 223 [hep-ph/0005122] [INSPIRE].
  50. [50]
    J. Polonyi, Lectures on the functional renormalization group method, Central Eur. J. Phys. 1 (2003) 1 [hep-th/0110026] [INSPIRE].ADSGoogle Scholar
  51. [51]
    J.M. Pawlowski, Aspects of the functional renormalisation group, Annals Phys. 322 (2007) 2831 [hep-th/0512261] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    H. Gies, Introduction to the functional RG and applications to gauge theories, Lect. Notes Phys. 852 (2012) 287 [hep-ph/0611146] [INSPIRE].
  53. [53]
    B. Delamotte, An introduction to the nonperturbative renormalization group, Lect. Notes Phys. 852 (2012) 49 [cond-mat/0702365] [INSPIRE].
  54. [54]
    O.J. Rosten, Fundamentals of the exact renormalization group, Phys. Rept. 511 (2012) 177 [arXiv:1003.1366] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    J. Braun, Fermion interactions and universal behavior in strongly interacting theories, J. Phys. G 39 (2012) 033001 [arXiv:1108.4449] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    A. Eichhorn, L. Janssen and M.M. Scherer, Critical O(N ) models above four dimensions: small-N solutions and stability, Phys. Rev. D 93 (2016) 125021 [arXiv:1604.03561] [INSPIRE].ADSMathSciNetGoogle Scholar
  57. [57]
    H. Gies, S. Rechenberger, M.M. Scherer and L. Zambelli, An asymptotic safety scenario for gauged chiral Higgs-Yukawa models, Eur. Phys. J. C 73 (2013) 2652 [arXiv:1306.6508] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    J. Braun, H. Gies and D.D. Scherer, Asymptotic safety: a simple example, Phys. Rev. D 83 (2011) 085012 [arXiv:1011.1456] [INSPIRE].ADSGoogle Scholar
  59. [59]
    H. Gies and M.M. Scherer, Asymptotic safety of simple Yukawa systems, Eur. Phys. J. C 66 (2010) 387 [arXiv:0901.2459] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    H. Gies, Renormalizability of gauge theories in extra dimensions, Phys. Rev. D 68 (2003) 085015 [hep-th/0305208] [INSPIRE].ADSGoogle Scholar
  61. [61]
    D.F. Litim, Optimized renormalization group flows, Phys. Rev. D 64 (2001) 105007 [hep-th/0103195] [INSPIRE].ADSGoogle Scholar
  62. [62]
    M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181 [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Phys. C 69 (1996) 687 [hep-th/9506019] [INSPIRE].MathSciNetGoogle Scholar
  64. [64]
    M. D’Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    M. Reuter and C. Wetterich, Gluon condensation in nonperturbative flow equations, Phys. Rev. D 56 (1997) 7893 [hep-th/9708051] [INSPIRE].ADSGoogle Scholar
  66. [66]
    D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    F. Freire, D.F. Litim and J.M. Pawlowski, Gauge invariance and background field formalism in the exact renormalization group, Phys. Lett. B 495 (2000) 256 [hep-th/0009110] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    M. Reuter and C. Wetterich, Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity, Phys. Rev. D 65 (2002) 025013 [hep-th/0108040] [INSPIRE].ADSMathSciNetGoogle Scholar
  70. [70]
    S.P. Robinson and F. Wilczek, Gravitational correction to running of gauge couplings, Phys. Rev. Lett. 96 (2006) 231601 [hep-th/0509050] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  71. [71]
    A.R. Pietrykowski, Gauge dependence of gravitational correction to running of gauge couplings, Phys. Rev. Lett. 98 (2007) 061801 [hep-th/0606208] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  73. [73]
    D.J. Toms, Quantum gravity and charge renormalization, Phys. Rev. D 76 (2007) 045015 [arXiv:0708.2990] [INSPIRE].ADSMathSciNetGoogle Scholar
  74. [74]
    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].ADSCrossRefGoogle Scholar
  75. [75]
    D.J. Toms, Quantum gravitational contributions to quantum electrodynamics, Nature 468 (2010) 56 [arXiv:1010.0793] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    D.J. Toms, Quadratic divergences and quantum gravitational contributions to gauge coupling constants, Phys. Rev. D 84 (2011) 084016 [INSPIRE].ADSGoogle Scholar
  77. [77]
    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].ADSGoogle Scholar
  78. [78]
    J. Ellis and N.E. Mavromatos, On the interpretation of gravitational corrections to gauge couplings, Phys. Lett. B 711 (2012) 139 [arXiv:1012.4353] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    D.J. Toms, Quantum gravity, gauge coupling constants and the cosmological constant, Phys. Rev. D 80 (2009) 064040 [arXiv:0908.3100] [INSPIRE].ADSMathSciNetGoogle Scholar
  80. [80]
    O. Lauscher and M. Reuter, Fractal spacetime structure in asymptotically safe gravity, JHEP 10 (2005) 050 [hep-th/0508202] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  81. [81]
    M. Reuter and F. Saueressig, Fractal space-times under the microscope: a renormalization group view on Monte Carlo data, JHEP 12 (2011) 012 [arXiv:1110.5224] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  82. [82]
    G. Calcagni, A. Eichhorn and F. Saueressig, Probing the quantum nature of spacetime by diffusion, Phys. Rev. D 87 (2013) 124028 [arXiv:1304.7247] [INSPIRE].ADSGoogle Scholar
  83. [83]
    S. Carlip, Spontaneous dimensional reduction in quantum gravity, Int. J. Mod. Phys. D 25 (2016) 1643003 [arXiv:1605.05694] [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    J. Ambjørn, J. Jurkiewicz and R. Loll, Spectral dimension of the universe, Phys. Rev. Lett. 95 (2005) 171301 [hep-th/0505113] [INSPIRE].ADSCrossRefGoogle Scholar
  85. [85]
    P. Hořava, Spectral dimension of the universe in quantum gravity at a Lifshitz point, Phys. Rev. Lett. 102 (2009) 161301 [arXiv:0902.3657] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  86. [86]
    S. Carlip, Dimensional reduction in causal set gravity, Class. Quant. Grav. 32 (2015) 232001 [arXiv:1506.08775] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  87. [87]
    M. Shaposhnikov and C. Wetterich, Asymptotic safety of gravity and the Higgs boson mass, Phys. Lett. B 683 (2010) 196 [arXiv:0912.0208] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    F. Bezrukov, M. Yu. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs boson mass and new physics, JHEP 10 (2012) 140 [arXiv:1205.2893] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    S. Lippoldt, to appear.Google Scholar
  90. [90]
    P. Donà and R. Percacci, Functional renormalization with fermions and tetrads, Phys. Rev. D 87 (2013) 045002 [arXiv:1209.3649] [INSPIRE].ADSGoogle Scholar
  91. [91]
    A. Eichhorn and A. Held, in preparation.Google Scholar
  92. [92]
    H. Gies, B. Knorr and S. Lippoldt, Generalized parametrization dependence in quantum gravity, Phys. Rev. D 92 (2015) 084020 [arXiv:1507.08859] [INSPIRE].ADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany

Personalised recommendations