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QED coupled to QEG

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Abstract

We discuss the non-perturbative renormalization group flow of Quantum Electrodynamics (QED) coupled to Quantum Einstein Gravity (QEG) and explore the possibilities for defining its continuum limit at a fixed point that would lead to a non-trivial, i.e. interacting field theory. We find two fixed points suitable for the Asymptotic Safety construction. In the first case, the fine-structure constant α vanishes at the fixed point and its infrared (“renormalized”) value is a free parameter not determined by the theory itself. In the second case, the fixed point value of α is non-zero, and its infrared value is a computable prediction of the theory.

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References

  1. K.G. Wilson and J.B. Kogut, The renormalization group and the ϵ-expansion, Phys. Rept. 12 (1974) 75 [SPIRES].

    Article  ADS  Google Scholar 

  2. K.G. Wilson, The renormalization group: critical phenomena and the Kondo problem, Rev. Mod. Phys. 47 (1975) 773 [SPIRES].

    Article  ADS  Google Scholar 

  3. G. Parisi, The theory of nonrenormalizable interactions. 1. The large-N expansion, Nucl. Phys. B 100 (1975) 368 [SPIRES].

    Article  ADS  Google Scholar 

  4. G. Parisi, Symanzik’s improvement program, Nucl. Phys. B 254 (1985) 58 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. K. Gawędzki and A. Kupiainen, Renormalization of a nonrenormalizable quantum field theory, Nucl. Phys. B 262 (1985) 33 [SPIRES].

    ADS  Google Scholar 

  6. K. Gawędzki and A. Kupiainen, Exact renormalization for the Gross-Neveu model of quantum fields, Phys. Rev. Lett. 54 (1985) 2191 [SPIRES].

    Article  ADS  Google Scholar 

  7. K. Gawędzki and A. Kupiainen, Renormalizing the nonrenormalizable, Phys. Rev. Lett. 55 (1985) 363 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. B. Rosenstein, B. Warr and S.H. Park, Dynamical symmetry breaking in four Fermi interaction models, Phys. Rept. 205 (1991) 59 [SPIRES].

    Article  ADS  Google Scholar 

  9. C. de Calan, P.A. Faria da Veiga, J. Magnen and R. Sénéor, Constructing the three-dimensional Gross-Neveu model with a large number of flavor components, Phys. Rev. Lett. 66 (1991) 3233 [SPIRES].

    Article  ADS  Google Scholar 

  10. H. Römer, Mechanisms of spontaneous mass generation and solvable models, Acta Phys. Austriaca 45 (1976) 125 [SPIRES].

    MathSciNet  Google Scholar 

  11. H. Römer, Spontaneous mass generation, renormalization group and solvable U(N) symmetric models, Acta Phys. Austriaca, Suppl. 14 (1975) 521 [SPIRES].

    Google Scholar 

  12. M. Gell-Mann and F.E. Low, Quantum electrodynamics at small distances, Phys. Rev. 95 (1954) 1300 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. M. Göckeler et al., Is there a Landau pole problem in QED?, Phys. Rev. Lett. 80 (1998) 4119 [hep-th/9712244] [SPIRES].

    Article  ADS  Google Scholar 

  14. S. Kim, J.B. Kogut and M.-P. Lombardo, On the triviality of textbook quantum electrodynamics, Phys. Lett. B 502 (2001) 345 [hep-lat/0009029] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. S. Kim, J.B. Kogut and M.-P. Lombardo, Gauged Nambu-Jona Lasinio studies of the triviality of quantum electrodynamics, Phys. Rev. D 65 (2002) 054015 [hep-lat/0112009] [SPIRES].

    ADS  Google Scholar 

  16. H. Gies and J. Jaeckel, Renormalization flow of QED, Phys. Rev. Lett. 93 (2004) 110405 [hep-ph/0405183] [SPIRES].

    Article  ADS  Google Scholar 

  17. G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Ann. Poincaré Phys. Theor. A 20 (1974) 69.

    MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  20. S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: an Einstein Centenary Survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979) [SPIRES].

    Google Scholar 

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

  22. S. Weinberg, Effective field theory, past and future, PoS(CD09)001 [arXiv:0908.1964] [SPIRES].

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

    MathSciNet  ADS  Google Scholar 

  24. 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 

  25. 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 

  26. O. Lauscher and M. Reuter, Flow equation of quantum Einstein gravity in a higher-derivative truncation, Phys. Rev. D 66 (2002) 025026 [hep-th/0205062] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  27. 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 

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

    ADS  Google Scholar 

  29. 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 

  30. 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 

  31. 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 

  32. 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  MathSciNet  ADS  Google Scholar 

  33. D. Benedetti, K. Groh, P.F. Machado and F. Saueressig, The universal RG machine, arXiv:1012.3081 [SPIRES].

  34. M. Reuter and F. Saueressig, Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity, in Geometric and topological methods for quantum field theory, H. Ocampo, E. Pariguan and S. Paycha eds., Cambridge University Press, Cambridge U.K. (2010) [arXiv:0708.1317] [SPIRES].

    Google Scholar 

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

    Google Scholar 

  36. R. Percacci, Asymptotic safety, in Approaches to quantum gravity: towards a new understanding of space, time and matter, D. Oriti ed., Cambridge University Press, Cambridge U.K. (2009) [arXiv:0709.3851] [SPIRES].

    Google Scholar 

  37. 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 

  38. S.P. Robinson, Two quantum effects in the theory of gravitation, Ph.D. Thesis, MIT, (2005).

  39. 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 

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

    MathSciNet  ADS  Google Scholar 

  41. 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 

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

    Article  ADS  MATH  Google Scholar 

  43. 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 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  46. M.M. Anber, J.F. Donoghue and M. El-Houssieny, Running couplings and operator mixing in the gravitational corrections to coupling constants, arXiv:1011.3229 [SPIRES].

  47. J. Ellis and N.E. Mavromatos, On the interpretation of gravitational corrections to gauge couplings, arXiv:1012.4353 [SPIRES].

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

    Article  ADS  Google Scholar 

  49. J.E. Daum, U. Harst and M. Reuter, Non-perturbative QEG corrections to the Yang-Mills β-function, arXiv:1005.1488 [SPIRES].

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  52. 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 

  53. M. Shaposhnikov and C. Wetterich, Asymptotic safety of gravity and the Higgs boson mass, Phys. Lett. B 683 (2010) 196 [arXiv:0912.0208] [SPIRES].

    ADS  Google Scholar 

  54. U. Amaldi, W. de Boer, P.H. Frampton, H. Fürstenau and J.T. Liu, Consistency checks of grand unified theories, Phys. Lett. B 281 (1992) 374 [SPIRES].

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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ArXiv ePrint: 1101.6007

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Harst, U., Reuter, M. QED coupled to QEG. J. High Energ. Phys. 2011, 119 (2011). https://doi.org/10.1007/JHEP05(2011)119

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