Asymptotic safety: A simple example

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 83, Issue 8, 2011, Pages

  Braun, Jens ^a   Gies, Holger ^a   Scherer, Daniel D ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960752008     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.83.085012     Document Type: Article

References (89)

1. L.D. Landau, in Niels Bohr and the Development of Physics, edited by, W. Pauli, (Pergamon Press, London, 1955);
2. M. Gell-Mann and F.E. Low, Phys. Rev. 95, 1300 (1954); PHRVAO 0031-899X 10.1103/PhysRev.95.1300
3. M. Gockeler, Phys. Rev. Lett. 80, 4119 (1998); PRLTAO 0031-9007 10.1103/PhysRevLett.80.4119
4. H. Gies and J. Jaeckel, Phys. Rev. Lett. 93, 110405 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.110405
5. E. Brezin, J.C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena (London, Academic Press, 1976), Vol. 6, pp. 125-247;
6. M. Luscher and P. Weisz, Nucl. Phys. NUPBBO 0550-3213 B290, 25 (1987); 10.1016/0550-3213(87)90177-5
7. U. Wolff, Phys. Rev. D PRVDAQ 1550-7998 79, 105002 (2009); 10.1103/PhysRevD.79.105002
8. S. Weinberg, Lectures Presented at the International School of Subnuclear Physics, Erice Subnucl. Phys. (1976), 1.
9. S. Weinberg, arXiv:hep-th/9702027;
10. S. Weinberg, arXiv:0903.0568;
11. M. Niedermaier and M. Reuter, Living Rev. Relativity 1433-8351 9, 5 (2006);
12. R. Percacci, in Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter, edited by, D. Oriti, (Cambridge University Press, Cambridge, England, 2009).
13. O.J. Rosten, arXiv:1003.1366.
14. C. Wetterich, Phys. Lett. B 301, 90 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)90726-X
15. M. Reuter, Phys. Rev. D PRVDAQ 0556-2821 57, 971 (1998). 10.1103/PhysRevD.57.971
16. D. Dou and R. Percacci, Classical Quantum Gravity CQGRDG 0264-9381 15, 3449 (1998); 10.1088/0264-9381/15/11/011 (Pubitemid 128155146)
17. W. Souma, Prog. Theor. Phys. 102, 181 (1999); PTPKAV 0033-068X 10.1143/PTP.102.181
18. M. Reuter and F. Saueressig, Phys. Rev. D PRVDAQ 0556-2821 65, 065016 (2002). 10.1103/PhysRevD.65.065016 (Pubitemid 44628499)
19. O. Lauscher and M. Reuter, Phys. Rev. D PRVDAQ 0556-2821 65, 025013 (2001). 10.1103/PhysRevD.65.025013
20. D.F. Litim, Phys. Rev. Lett. 92, 201301 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.201301
21. A. Codello and R. Percacci, Phys. Rev. Lett. 97, 221301 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.97.221301 (Pubitemid 44826912)
22. A. Codello, R. Percacci, and C. Rahmede, Int. J. Mod. Phys. A 23, 143 (2008); IMPAEF 0217-751X 10.1142/S0217751X08038135
23. P.F. Machado and F. Saueressig, Phys. Rev. D PRVDAQ 1550-7998 77, 124045 (2008); 10.1103/PhysRevD.77.124045
24. A. Eichhorn, H. Gies, and M.M. Scherer, Phys. Rev. D PRVDAQ 1550-7998 80, 104003 (2009); 10.1103/PhysRevD.80.104003
25. K. Groh and F. Saueressig, J. Phys. A 1751-8113 43, 365403 (2010); 10.1088/1751-8113/43/36/365403
26. A. Eichhorn and H. Gies, Phys. Rev. D PRVDAQ 1550-7998 81, 104010 (2010). 10.1103/PhysRevD.81.104010
27. J. Ambjorn, J. Jurkiewicz, and R. Loll, Phys. Rev. D PRVDAQ 1550-7998 72, 064014 (2005). 10.1103/PhysRevD.72.064014
28. H. Gies, J. Jaeckel, and C. Wetterich, Phys. Rev. D PRVDAQ 0556-2821 69, 105008 (2004). 10.1103/PhysRevD.69.105008
29. H. Gies and M.M. Scherer, Eur. Phys. J. C 66, 387 (2010). EPCFFB 1434-6044 10.1140/epjc/s10052-010-1256-z
30. H. Gies, S. Rechenberger, and M.M. Scherer, Eur. Phys. J. C 66, 403 (2010). EPCFFB 1434-6044 10.1140/epjc/s10052-010-1257-y
31. R. Percacci and O. Zanusso, Phys. Rev. D PRVDAQ 1550-7998 81, 065012 (2010); 10.1103/PhysRevD.81.065012
32. M. Fabbrichesi, Phys. Rev. D PRVDAQ 1550-7998 83, 025016 (2011). 10.1103/PhysRevD.83.025016
33. H. Gies, Phys. Rev. D PRVDAQ 0556-2821 68, 085015 (2003). 10.1103/PhysRevD.68.085015 (Pubitemid 44642091)
34. P. Fischer and D.F. Litim, in Fixed Points of Quantum Gravity in Higher Dimensions, edited by, AIP Conf. Proc. No. 861 (AIP, New York, 2006) pg. 336);
35. P. Fischer D.F. Litim Phys. Lett. B 638, 497 (2006). PYLBAJ 0370-2693 10.1016/j.physletb.2006.05.073 (Pubitemid 43963272)
36. D.J. Gross and A. Neveu, Phys. Rev. D PRVDAQ 0556-2821 10, 3235 (1974). 10.1103/PhysRevD.10.3235
37. B. Rosenstein, B.J. Warr, and S.H. Park, Phys. Rev. Lett. 62, 1433 (1989); PRLTAO 0031-9007 10.1103/PhysRevLett.62.1433
38. K. Gawedzki and A. Kupiainen, Phys. Rev. Lett. 55, 363 (1985); PRLTAO 0031-9007 10.1103/PhysRevLett.55.363
39. C. de Calan, P.A. Faria da Veiga, J. Magnen, and R. Seneor, Phys. Rev. Lett. 66, 3233 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.66.3233
40. J. Zinn-Justin, Nucl. Phys. NUPBBO 0550-3213 B367, 105 (1991). 10.1016/0550-3213(91)90043-W
41. A. Hasenfratz, P. Hasenfratz, K. Jansen, J. Kuti, and Y. Shen, Nucl. Phys. NUPBBO 0550-3213 B365, 79 (1991). 10.1016/0550-3213(91)90607-Y
42. S. Hands, A. Kocic, and J.B. Kogut, Ann. Phys. (N.Y.) APNYA6 0003-4916 224, 29 (1993). 10.1006/aphy.1993.1039
43. L. Karkkainen, R. Lacaze, P. Lacock, and B. Petersson, Nucl. Phys. NUPBBO 0550-3213 B415, 781 (1994). 10.1016/0550-3213(94)90309-3
44. G. Gat, A. Kovner, and B. Rosenstein, Nucl. Phys. NUPBBO 0550-3213 B385, 76 (1992). 10.1016/0550-3213(92)90095-S
45. J.A. Gracey, Int. J. Mod. Phys. A 9, 727 (1994); IMPAEF 0217-751X 10.1142/S0217751X94000340
46. A.N. Vasiliev, S.E. Derkachov, N.A. Kivel, and A.S. Stepanenko, Theor. Math. Phys. 94, 127 (1993). TMPHAH 0040-5779 10.1007/BF01019324
47. E. Focht, J. Jersak, and J. Paul, Phys. Rev. D PRVDAQ 0556-2821 53, 4616 (1996); 10.1103/PhysRevD.53.4616
48. T. Reisz, Lect. Notes Phys. LNPHA4 0075-8450 508, 192 (1998); 10.1007/BFb0106886
49. E. Babaev, Phys. Lett. B 497, 323 (2001); PYLBAJ 0370-2693 10.1016/S0370-2693(00)01335-6 (Pubitemid 32063763)
50. L. Rosa, P. Vitale, and C. Wetterich, Phys. Rev. Lett. 86, 958 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.958 (Pubitemid 32169202)
51. F. Hofling, C. Nowak, and C. Wetterich, Phys. Rev. B PRBMDO 0163-1829 66, 205111 (2002). 10.1103/PhysRevB.66.205111
52. D.F. Litim and J.M. Pawlowski, The Exact Renormalization Group: Proceedings, edited by, A. Krasnitz, (World Scientific, Hackensack, New Jersey, 1999), p. 168;
53. C. Bagnuls and C. Bervillier, Phys. Rep. PRPLCM 0370-1573 348, 91 (2001); 10.1016/S0370-1573(00)00137-X
54. J. Polonyi, Central Eur. J. Phys. 1644-3608 1, 1 (2003); 10.2478/BF02475552
55. B. Delamotte, D. Mouhanna, and M. Tissier, Phys. Rev. B PRBMDO 0163-1829 69, 134413 (2004); 10.1103/PhysRevB.69.134413
56. J.M. Pawlowski, Ann. Phys. (N.Y.) APNYA6 0003-4916 322, 2831 (2007); 10.1016/j.aop.2007.01.007
57. H. Gies, arXiv:hep-ph/0611146;
58. B. Delamotte, arXiv:cond-mat/0702365.
59. J. Berges, N. Tetradis, and C. Wetterich, Phys. Rep. PRPLCM 0370-1573 363, 223 (2002). 10.1016/S0370-1573(01)00098-9
60. J. Jaeckel and C. Wetterich, Phys. Rev. D PRVDAQ 0556-2821 68, 025020 (2003). 10.1103/PhysRevD.68.025020 (Pubitemid 44628236)
61. J. Jaeckel, Ph.D. thesis, University of Heidelberg, 2003.
62. H. Gies, L. Janssen, S. Rechenberger, and M.M. Scherer, Phys. Rev. D PRVDAQ 1550-7998 81, 025009 (2010). 10.1103/PhysRevD.81.025009
63. D.F. Litim, Phys. Lett. B 486, 92 (2000). PYLBAJ 0370-2693 10.1016/S0370-2693(00)00748-6
64. D.F. Litim, Phys. Rev. D PRVDAQ 0556-2821 64, 105007 (2001). 10.1103/PhysRevD.64.105007
65. D.F. Litim, Int. J. Mod. Phys. A 16, 2081 (2001). IMPAEF 0217-751X 10.1142/S0217751X01004748
66. S. Hands, S. Kim, and J.B. Kogut, Nucl. Phys. NUPBBO 0550-3213 B442, 364 (1995); 10.1016/0550-3213(95)00136-0
67. V. Schon and M. Thies, Phys. Rev. D PRVDAQ 0556-2821 62, 096002 (2000). 10.1103/PhysRevD.62.096002
68. M. Thies and K. Urlichs, Phys. Rev. D PRVDAQ 0556-2821 67, 125015 (2003). 10.1103/PhysRevD.67.125015 (Pubitemid 44652518)
69. M. Thies, Phys. Rev. D PRVDAQ 0556-2821 69, 067703 (2004); 10.1103/PhysRevD.69.067703 (Pubitemid 44652865)
70. G. Basar and G.V. Dunne, Phys. Rev. Lett. 100, 200404 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.200404 (Pubitemid 351718013)
71. G. Basar and G.V. Dunne, Phys. Rev. D PRVDAQ 1550-7998 78, 065022 (2008). 10.1103/PhysRevD.78.065022
72. P. Castorina, M. Mazza, and D. Zappala, Phys. Lett. B 567, 31 (2003). PYLBAJ 0370-2693 10.1016/j.physletb.2003.06.005
73. R. Stratonovich, Dokl. Akad. Nauk SSSR DASBAQ 0002-3264 115, 1097 (1957).
74. J. Hubbard, Phys. Rev. Lett. 3, 77 (1959). PRLTAO 0031-9007 10.1103/PhysRevLett.3.77
75. D. Nickel, Phys. Rev. D PRVDAQ 1550-7998 80, 074025 (2009). 10.1103/PhysRevD.80.074025
76. T. Kojo, Y. Hidaka, L. McLerran, and R.D. Pisarski, Nucl. Phys. A843, 37 (2010). NUPABL 0375-9474 10.1016/j.nuclphysa.2010.05.053
77. J. Zinn-Justin, Int. Ser. Monogr. Phys. ISMPFK 0950-5563 113, 1 (2002).
78. N. Tetradis and D.F. Litim, Nucl. Phys. NUPBBO 0550-3213 B464, 492 (1996). 10.1016/0550-3213(95)00642-7 (Pubitemid 126165625)
79. S. Diehl, H. Gies, J.M. Pawlowski, and C. Wetterich, Phys. Rev. A 76, 021602 (2007); PLRAAN 1050-2947 10.1103/PhysRevA.76.021602
80. S. Diehl H. Gies J.M. Pawlowski C. Wetterich Phys. Rev. A 76, 053627 (2007). PLRAAN 1050-2947 10.1103/PhysRevA.76.053627 (Pubitemid 350198395)
81. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, edited by, Jeffrey, and, Alan, (Academic Press, New York, 2000).
82. J. Braun, Phys. Rev. D PRVDAQ 1550-7998 81, 016008 (2010). 10.1103/PhysRevD.81.016008
83. N. Tetradis and C. Wetterich, Nucl. Phys. NUPBBO 0550-3213 B422, 541 (1994). 10.1016/0550-3213(94)90446-4
84. D.F. Litim and J.M. Pawlowski, Phys. Lett. B 516, 197 (2001). PYLBAJ 0370-2693 10.1016/S0370-2693(01)00922-4
85. D.F. Litim, Nucl. Phys. NUPBBO 0550-3213 B631, 128 (2002).
86. C. Bervillier, A. Juttner, and D.F. Litim, Nucl. Phys. NUPBBO 0550-3213 B783, 213 (2007). 10.1016/j.nuclphysb.2007.03.036
87. F. Benitez, Phys. Rev. E PLEEE8 1539-3755 80, 030103 (2009). 10.1103/PhysRevE.80.030103
88. D.F. Litim and D. Zappala, arXiv:1009.1948.
89. H. Gies and L. Janssen, Phys. Rev. D PRVDAQ 1550-7998 82, 085018 (2010). 10.1103/PhysRevD.82.085018