Fractal space-times under the microscope: A renormalization group view on Monte Carlo data

Journal of High Energy Physics

Volumn 2011, Issue 12, 2011, Pages

  Reuter, Martin ^a   Saueressig, Frank ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Lattice models of gravity; Models of quantum gravity; Nonperturbative effects; Renormalization group

Indexed keywords

EID: 84255187300     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP12(2011)012     Document Type: Article

References (84)

1. M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [INSPIRE].
2. 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).
3. S. Weinberg, Living with Infinities, arXiv:0903.0568 [INSPIRE].
4. S. Weinberg, Effective field theories - past and future, PoS(CD09)001.
5. D. Dou and R. Percacci, The running gravitational couplings, Class. Quant. Grav. 15 (1998) 3449 [hep-th/9707239] [INSPIRE].
6. W. Souma, Nontrivial ultraviolet fixed point in quantum gravity, Prog. Theor. Phys. 102 (1999) 181 [hep-th/9907027] [INSPIRE].
7. 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].
8. O. Lauscher and M. Reuter, Is quantum Einstein gravity nonperturbatively renormalizable?, Class. Quant. Grav. 19 (2002) 483 [hep-th/0110021] [INSPIRE].
9. O. Lauscher and M. Reuter, Towards nonperturbative renormalizability of quantum Einstein gravity, Int. J. Mod. Phys. A 17 (2002) 993 [hep-th/0112089] [INSPIRE].
10. 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].
11. 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] [INSPIRE].
12. 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] [INSPIRE].
13. D.F. Litim, Fixed points of quantum gravity, Phys. Rev. Lett. 92 (2004) 201301 [hep-th/0312114] [INSPIRE].
14. A. Bonanno and M. Reuter, Proper time flow equation for gravity, JHEP 02 (2005) 035 [hep-th/0410191] [INSPIRE].
15. 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] [INSPIRE].
16. M. Reuter and J.-M. Schwindt, Scale-dependent metric and causal structures in Quantum Einstein Gravity, JHEP 01 (2007) 049 [hep-th/0611294] [INSPIRE].
17. A. Codello and R. Percacci, Fixed points of higher derivative gravity, Phys. Rev. Lett. 97 (2006) 221301 [hep-th/0607128] [INSPIRE].
18. A. Codello, R. Percacci and C. Rahmede, Ultraviolet properties of f(R) Gravity, Int. J. Mod. Phys. A 23 (2008) 143 [arXiv:0705.1769] [INSPIRE].
19. P. Fischer and D.F. Litim, Fixed points of quantum gravity in extra dimensions, Phys. Lett. B 638 (2006) 497 [hep-th/0602203] [INSPIRE].
20. P.F. Machado and F. Saueressig, On the renormalization group flow of f(R)-gravity, Phys. Rev. D 77 (2008) 124045 [arXiv:0712.0445] [INSPIRE].
21. M. Reuter and H. Weyer, Background Independence and Asymptotic Safety in Conformally Reduced Gravity, Phys. Rev. D 79 (2009) 105005 [arXiv:0801.3287] [INSPIRE].
22. 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] [INSPIRE].
23. M. Reuter and H. Weyer, Conformal sector of Quantum Einstein Gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance, Phys. Rev. D 80 (2009) 025001 [arXiv:0804.1475] [INSPIRE].
24. P.F. Machado and R. Percacci, Conformally reduced quantum gravity revisited, Phys. Rev. D 80 (2009) 024020 [arXiv:0904.2510] [INSPIRE].
25. 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].
26. 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].
27. D. Benedetti, P.F. Machado and F. Saueressig, Taming perturbative divergences in asymptotically safe gravity, Nucl. Phys. B 824 (2010) 168 [arXiv:0902.4630] [INSPIRE].
28. D. Benedetti, P.F. Machado and F. Saueressig, Four-derivative interactions in asymptotically safe gravity, arXiv:0909.3265 [INSPIRE].
29. 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] [INSPIRE].
30. A. Eichhorn and H. Gies, Ghost anomalous dimension in asymptotically safe quantum gravity, Phys. Rev. D 81 (2010) 104010 [arXiv:1001.5033] [INSPIRE].
31. K. Groh and F. Saueressig, Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity, J. Phys. A 43 (2010) 365403 [arXiv:1001.5032] [INSPIRE].
32. 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] [INSPIRE].
33. E. Manrique and M. Reuter, Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety, Annals Phys. 325 (2010) 785 [arXiv:0907.2617] [INSPIRE].
34. E. Manrique, M. Reuter and F. Saueressig, Matter Induced Bimetric Actions for Gravity, Annals Phys. 326 (2011) 440 [arXiv:1003.5129] [INSPIRE].
35. E. Manrique, M. Reuter and F. Saueressig, Bimetric Renormalization Group Flows in Quantum Einstein Gravity, Annals Phys. 326 (2011) 463 [arXiv:1006.0099] [INSPIRE].
36. J.-E. Daum, U. Harst and M. Reuter, Running Gauge Coupling in Asymptotically Safe Quantum Gravity, JHEP 01 (2010) 084 [arXiv:0910.4938] [INSPIRE].
37. 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] [INSPIRE].
38. D. Benedetti, K. Groh, P.F. Machado and F. Saueressig, The Universal RG Machine, JHEP 06 (2011) 079 [arXiv:1012.3081] [INSPIRE].
39. E. Manrique, S. Rechenberger and F. Saueressig, Asymptotically Safe Lorentzian Gravity, Phys. Rev. Lett. 106 (2011) 251302 [arXiv:1102.5012] [INSPIRE].
40. M.R. Niedermaier, Gravitational Fixed Points from Perturbation Theory, Phys. Rev. Lett. 103 (2009) 101303 [INSPIRE].
41. P. Forgacs and M. Niedermaier, A Fixed point for truncated quantum Einstein gravity, hep-th/0207028 [INSPIRE].
42. M. Niedermaier, On the renormalization of truncated quantum Einstein gravity, JHEP 12 (2002) 066 [hep-th/0207143] [INSPIRE].
43. M. Niedermaier, Dimensionally reduced gravity theories are asymptotically safe, Nucl. Phys. B 673 (2003) 131 [hep-th/0304117] [INSPIRE].
44. M. Niedermaier, The Asymptotic safety scenario in quantum gravity: An Introduction, Class. Quant. Grav. 24 (2007) R171 [gr-qc/0610018] [INSPIRE].
45. M. Reuter and F. Saueressig, Functional Renormalization Group Equations, Asymptotic Safety and Quantum Einstein Gravity, arXiv:0708.1317 [INSPIRE].
46. O. Lauscher and M. Reuter, Asymptotic safety in quantum Einstein gravity: Nonperturbative renormalizability and fractal spacetime structure, hep-th/0511260 [INSPIRE].
47. O. Lauscher and M. Reuter, Quantum Einstein Gravity: Towards an Asymptotically Safe Field Theory of Gravity, in Approaches to Fundamental Physics, I.-O. Stamatescu and E. Seiler (eds.), Springer, Berlin (2007).
48. R. Charity et al., Investigations of three, four and five-particle exit channels of levels in light nuclei created using a 9C beam, Phys. Rev. C 84 (2011) 014320 [arXiv:1105.1144] [INSPIRE].
49. R. Percacci, Asymptotic Safety, arXiv:0709.3851 [INSPIRE].
50. 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] [INSPIRE].
51. A. Bonanno and M. Reuter, Entropy signature of the running cosmological constant, JCAP 08 (2007) 024 [arXiv:0706.0174] [INSPIRE].
52. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York (1977).
53. H. Kawai and M. Ninomiya, Renormalization Group and Quantum Gravity, Nucl. Phys. B 336 (1990) 115 [INSPIRE].
54. R. Floreanini and R. Percacci, Average effective potential for the conformal factor, Nucl. Phys. B 436 (1995) 141 [hep-th/9305172] [INSPIRE].
55. J. Ambjørn, J. Jurkiewicz and R. Loll, Emergence of a 4 - D world from causal quantum gravity, Phys. Rev. Lett. 93 (2004) 131301 [hep-th/0404156] [INSPIRE].
56. J. Ambjørn, J. Jurkiewicz and R. Loll, Quantum gravity as sum over spacetimes, Lect. Notes Phys. 807 (2010) 59 [arXiv:0906.3947] [INSPIRE].
57. J. Ambjørn, J. Jurkiewicz and R. Loll, Spectral dimension of the universe, Phys. Rev. Lett. 95 (2005) 171301 [hep-th/0505113] [INSPIRE].
58. J. Ambjørn, J. Jurkiewicz and R. Loll, Reconstructing the universe, Phys. Rev. D 72 (2005) 064014 [hep-th/0505154] [INSPIRE].
59. O. Lauscher and M. Reuter, Fractal spacetime structure in asymptotically safe gravity, JHEP 10 (2005) 050 [hep-th/0508202] [INSPIRE].
60. D. Benedetti and J. Henson, Spectral geometry as a probe of quantum spacetime, Phys. Rev. D 80 (2009) 124036 [arXiv:0911.0401] [INSPIRE].
61. J. Laiho and D. Coumbe, Evidence for Asymptotic Safety from Lattice Quantum Gravity, Phys. Rev. Lett. 107 (2011) 161301 [arXiv:1104.5505] [INSPIRE].
62. L. Modesto, Fractal structure of loop quantum gravity, Class. Quant. Grav. 26 (2009) 242002 [arXiv:0812.2214] [INSPIRE].
63. F. Caravelli and L. Modesto, Fractal Dimension in 3d Spin-Foams, arXiv:0905.2170 [INSPIRE].
64. E. Magliaro, C. Perini and L. Modesto, Fractal Space-Time from Spin-Foams, arXiv:0911.0437 [INSPIRE].
65. S. Carlip, Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?, arXiv:0909.3329 [INSPIRE].
66. S. Carlip, The Small Scale Structure of Spacetime, arXiv:1009.1136 [INSPIRE].
67. A. Connes, Noncommutative geometry and the standard model with neutrino mixing, JHEP 11 (2006) 081 [hep-th/0608226] [INSPIRE].
68. A.H. Chamseddine, A. Connes and M. Marcolli, Gravity and the standard model with neutrino mixing, Adv. Theor. Math. Phys. 11 (2007) 991 [hep-th/0610241] [INSPIRE].
69. D. Guido and T. Isola, Dimensions and singular traces for spectral triples, with applications to fractals, math/0202108.
70. *-algebras and metrics on the Cantor set, math/0309044.
71. D. Benedetti, Fractal properties of quantum spacetime, Phys. Rev. Lett. 102 (2009) 111303 [arXiv:0811.1396] [INSPIRE].
72. G. Calcagni, Fractal universe and quantum gravity, Phys. Rev. Lett. 104 (2010) 251301 [arXiv:0912.3142] [INSPIRE].
73. G. Calcagni, Quantum field theory, gravity and cosmology in a fractal universe, JHEP 03 (2010) 120 [arXiv:1001.0571] [INSPIRE].
74. G. Calcagni, Gravity on a multifractal, Phys. Lett. B 697 (2011) 251 [arXiv:1012.1244] [INSPIRE].
75. M. Arzano, G. Calcagni, D. Oriti and M. Scalisi, Fractional and noncommutative spacetimes, arXiv:1107.5308 [INSPIRE].
76. G. Calcagni, Geometry of fractional spaces, arXiv:1106.5787 [INSPIRE].
77. G. Calcagni, Geometry and field theory in multi-fractional spacetime, arXiv:1107.5041 [INSPIRE].
78. E. Akkermans, G.V. Dunne and A. Teplyaev, Thermodynamics of photons on fractals, Phys. Rev. Lett. 105 (2010) 230407 [arXiv:1010.1148] [INSPIRE].
79. E. Akkermans, G.V. Dunne and A. Teplyaev, Physical Consequences of Complex Dimensions of Fractals, Europhys. Lett. 88 (2009) 40007 [arXiv:0903.3681] [INSPIRE].
80. C.T. Hill, Fractal theory space: Space-time of noninteger dimensionality, Phys. Rev. D 67 (2003) 085004 [hep-th/0210076] [INSPIRE].
81. D. ben-Avraham and S. Havlin, Diffusion and reactions in fractals and disordered systems, Cambridge University Press, Cambridge U.K. (2004).
82. S. Alexander and R. Orbach, Density of states on fractals: "fractons", J. Phys. (Paris) Lett. 43 (1982) L625.
83. M. Reuter and H. Weyer, Quantum gravity at astrophysical distances?, JCAP 12 (2004) 001 [hep-th/0410119] [INSPIRE].
84. T.P. Sotiriou, M. Visser and S. Weinfurtner, Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations, Phys. Rev. Lett. 107 (2011) 131303 [arXiv:1105.5646] [INSPIRE].