Quantum geometry of 2D gravity coupled to unitary matter

Nuclear Physics B

Volumn 497, Issue 1-2, 1997, Pages 445-475

  Ambjorn J ^a   Anagnostopoulos, K N ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Dynamical triangulations; Lattice gravity; Non critical strings; Quantum gravity

Indexed keywords

EID: 0031582607     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00259-9     Document Type: Article

References (55)

1. [1] V. Knizhnik, A. Polyakov and A. Zamolodchikov, Mod. Phys. Lett. A 3 (1988) 819.
2. [2] F. David, Mod. Phys. Lett. A 3 (1988) 1651; J. Distler and H. Kawai, Nucl. Phys. B 321 (1989) 509.
3. [2] F. David, Mod. Phys. Lett. A 3 (1988) 1651; J. Distler and H. Kawai, Nucl. Phys. B 321 (1989) 509.
4. [3] H. Kawai, N. Kawamoto, T. Mogami and Y. Watabiki, Phys. Lett. B 306 (1993) 19.
5. [4] J. Ambjørn and Y. Watabiki, Nucl. Phys. B 445 (1995) 129.
6. [5] S. Catterall, G. Thorleifsson, M. Bowick and V. John, Phys. Lett. B 354 (1995) 58.
7. [6] J. Ambjørn, J. Jurkiewicz and Y. Watabiki, Nucl. Phys. B 454 (1995) 313.
8. [7] J. Distler, Z. Hlousek and H. Kawai, Int. J. Mod. Phys. A 5 (1990) 1093.
9. [8] J. Ambjørn, B. Durhuus and J. Fröhlich, Nucl. Phys. B 257 (1985) 433; B 270 (1986) 457; B 275 (1986) 161-184; J. Ambjøm, B. Durhuus J. Fröhlich and P. Orland, B 270 (1986) 457;
10. [8] J. Ambjørn, B. Durhuus and J. Fröhlich, Nucl. Phys. B 257 (1985) 433; B 270 (1986) 457; B 275 (1986) 161-184; J. Ambjøm, B. Durhuus J. Fröhlich and P. Orland, B 270 (1986) 457;
11. [8] J. Ambjørn, B. Durhuus and J. Fröhlich, Nucl. Phys. B 257 (1985) 433; B 270 (1986) 457; B 275 (1986) 161-184; J. Ambjøm, B. Durhuus J. Fröhlich and P. Orland, B 270 (1986) 457;
12. [8] J. Ambjørn, B. Durhuus and J. Fröhlich, Nucl. Phys. B 257 (1985) 433; B 270 (1986) 457; B 275 (1986) 161-184; J. Ambjøm, B. Durhuus J. Fröhlich and P. Orland, B 270 (1986) 457;
13. F. David, Nucl. Phys. B 257 (1985) 45, 543;
14. V.A. Kazakov, I. Kostov and A.A. Migdal, Phys. Lett. B 157 (1985) 295;
15. Nucl. Phys. B 275 (1986) 641.
16. [9] J. Ambjørn, K. Anagnostopoulos, L. Jensen, T. Ichihara, N. Kawamoto, K. Yotsuji and Y. Watabiki, Phys. Lett. B 397 (1997) 177.
17. [10] J. Ambjørn, K. Anagnostopoulos, L. Jensen, T. Ichihara, N. Kawamoto, K. Yotsuji and Y. Watabiki, to appear.
18. [11] J. Ambjørn, K. Anagnostopoulos, U. Magnea and G. Thorleifsson, Phys. Lett. B 388 (1996) 713.
19. [12] J. Ambjøm, K. Anagnostopoulos, U. Magnea and G. Thorleifsson, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 725.
20. [13] N. Kawamoto, V.A. Kazakov, Y. Saeki and Y. Watabiki, Phys. Rev. Lett. 68 (1992) 2113.
21. [14] M.G. Harris and J. Ambjørn, Nucl. Phys. B 474 (1996) 575.
22. [15] F. David, Nucl. Phys. B 368 (1992) 671.
23. [16] N. Kawamoto, Y. Saeki and Y. Watabiki, unpublished; Y. Watabiki, Prog. Theor. Phys. Suppl. 114 (1993) 1; N. Kawamoto, in Nishinomiya 1992, Proceedings, Quantum gravity, 112, ed. K. Kikkawa and M. Ninomiya (World Scientific, Singapore); in First Asia-Pacific Winter School for Theoretical Physics 1993, Proceedings, Current Topics in Theoretical Physics, ed. Y.M. Cho (World Scientific, Singapore).
24. [16] N. Kawamoto, Y. Saeki and Y. Watabiki, unpublished; Y. Watabiki, Prog. Theor. Phys. Suppl. 114 (1993) 1; N. Kawamoto, in Nishinomiya 1992, Proceedings, Quantum gravity, 112, ed. K. Kikkawa and M. Ninomiya (World Scientific, Singapore); in First Asia-Pacific Winter School for Theoretical Physics 1993, Proceedings, Current Topics in Theoretical Physics, ed. Y.M. Cho (World Scientific, Singapore).
25. [16] N. Kawamoto, Y. Saeki and Y. Watabiki, unpublished; Y. Watabiki, Prog. Theor. Phys. Suppl. 114 (1993) 1; N. Kawamoto, in Nishinomiya 1992, Proceedings, Quantum gravity, 112, ed. K. Kikkawa and M. Ninomiya (World Scientific, Singapore); in First Asia-Pacific Winter School for Theoretical Physics 1993, Proceedings, Current Topics in Theoretical Physics, ed. Y.M. Cho (World Scientific, Singapore).
26. [16] N. Kawamoto, Y. Saeki and Y. Watabiki, unpublished; Y. Watabiki, Prog. Theor. Phys. Suppl. 114 (1993) 1; N. Kawamoto, in Nishinomiya 1992, Proceedings, Quantum gravity, 112, ed. K. Kikkawa and M. Ninomiya (World Scientific, Singapore); in First Asia-Pacific Winter School for Theoretical Physics 1993, Proceedings, Current Topics in Theoretical Physics, ed. Y.M. Cho (World Scientific, Singapore).
27. [17] Y. Watabiki, Nucl. Phys. B 441 (1995) 119; Prog. Theor. Phys. Suppl. 114 (1993) 1.
28. [17] Y. Watabiki, Nucl. Phys. B 441 (1995) 119; Prog. Theor. Phys. Suppl. 114 (1993) 1.
29. [18] N. Ishibashi and H. Kawai, Phys. Lett. B 314 (1993) 190; B 322 (1994) 67; M. Fukuma, N. Ishibashi, H. Kawai and M. Ninomiya, Nucl. Phys. B 427 (1994) 139.
30. [18] N. Ishibashi and H. Kawai, Phys. Lett. B 314 (1993) 190; B 322 (1994) 67; M. Fukuma, N. Ishibashi, H. Kawai and M. Ninomiya, Nucl. Phys. B 427 (1994) 139.
31. [18] N. Ishibashi and H. Kawai, Phys. Lett. B 314 (1993) 190; B 322 (1994) 67; M. Fukuma, N. Ishibashi, H. Kawai and M. Ninomiya, Nucl. Phys. B 427 (1994) 139.
32. [19] N. Tsuda and T. Yukawa, Phys. Lett. B 305 (1993) 223; A. Fujitsu, N. Tsuda and T. Yukawa, 2D Quantum Gravity - Three States of Surfaces, KEK-CP-029 (hep-lat/9603013).
33. [19] N. Tsuda and T. Yukawa, Phys. Lett. B 305 (1993) 223; A. Fujitsu, N. Tsuda and T. Yukawa, 2D Quantum Gravity - Three States of Surfaces, KEK-CP-029 (hep-lat/9603013).
34. [20] J. Ambjørn, B. Durhuus and T. Jonsson, Phys. Lett. B 244 (1990) 403; Mod. Phys. Lett. A 6 (1991) 1133.
35. [20] J. Ambjørn, B. Durhuus and T. Jonsson, Phys. Lett. B 244 (1990) 403; Mod. Phys. Lett. A 6 (1991) 1133.
36. [21] J. Jurkiewicz, A. Krzywicki, B. Petersson and B. Soderberg, Phys. Lett. B 213 (1988) 511; C.F. Baillie and D.A. Johnston, Phys. Lett. B 286 (1992) 44; S. Catterall, J. Kogut and R. Renken, Phys. Lett. B 292 (1992) 277; J. Ambjørn, B. Durhuus, T. Jonsson and G. Thorleifsson, Nucl. Phys. B 398 (1993) 568.
37. [21] J. Jurkiewicz, A. Krzywicki, B. Petersson and B. Soderberg, Phys. Lett. B 213 (1988) 511; C.F. Baillie and D.A. Johnston, Phys. Lett. B 286 (1992) 44; S. Catterall, J. Kogut and R. Renken, Phys. Lett. B 292 (1992) 277; J. Ambjørn, B. Durhuus, T. Jonsson and G. Thorleifsson, Nucl. Phys. B 398 (1993) 568.
38. [21] J. Jurkiewicz, A. Krzywicki, B. Petersson and B. Soderberg, Phys. Lett. B 213 (1988) 511; C.F. Baillie and D.A. Johnston, Phys. Lett. B 286 (1992) 44; S. Catterall, J. Kogut and R. Renken, Phys. Lett. B 292 (1992) 277; J. Ambjørn, B. Durhuus, T. Jonsson and G. Thorleifsson, Nucl. Phys. B 398 (1993) 568.
39. [21] J. Jurkiewicz, A. Krzywicki, B. Petersson and B. Soderberg, Phys. Lett. B 213 (1988) 511; C.F. Baillie and D.A. Johnston, Phys. Lett. B 286 (1992) 44; S. Catterall, J. Kogut and R. Renken, Phys. Lett. B 292 (1992) 277; J. Ambjørn, B. Durhuus, T. Jonsson and G. Thorleifsson, Nucl. Phys. B 398 (1993) 568.
40. [22] J. Ambjørn, G. Thorleifsson and M. Wexler, Nucl. Phys. B 439 (1995) 187.
41. [23] H. Aoki, H. Kawai, J. Nishimura and A. Tsuchiya, Nucl. Phys. B 474 (1996) 512.
42. [24] N.D. Hari Dass, B.E. Hanlon and T. Yukawa, Phys. Lett. B 368 (1996) 55.
43. [25] D.V. Boulatov and V.A. Kazakov, Phys. Lett. B 184 (1987) 247.
44. [26] J.M. Daul, Q-states Potts Model on a Random Planar Lattice, LPTENS 94 (hep-th/9502014).
45. [27] Y. Watabiki, Fractal Structure of Space-Time in Two-Dimensional Quantum Gravity, presented at "Frontiers in Quantum Field Theory" in honor of the 60th birthday of Prof. K. Kikkawa, Toyonaka, Japan, 14-17 December 1995, TIT/HEP-333 (hep-th/9605185).
46. [28] B.V. de Bakker and J. Smit, Nucl. Phys. B 454 (1995) 343; P. Bialas, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 739.
47. [28] B.V. de Bakker and J. Smit, Nucl. Phys. B 454 (1995) 343; P. Bialas, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 739.
48. [29] G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, EPI-865-16-86 (1986); J. Comput. Phys. 97 (1991) 566; N.Z. Akopov, G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, J. Comput. Phys. 97 (1991) 573. [30] M. Lüscher, Comput. Phys. Commun. 79 (1994) 100; F. James, Comput. Phys. Commun. 79 (1994) 111; 97 (1996) 357 (E).
49. [29] G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, EPI-865-16-86 (1986); J. Comput. Phys. 97 (1991) 566; N.Z. Akopov, G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, J. Comput. Phys. 97 (1991) 573. [30] M. Lüscher, Comput. Phys. Commun. 79 (1994) 100; F. James, Comput. Phys. Commun. 79 (1994) 111; 97 (1996) 357 (E).
50. [29] G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, EPI-865-16-86 (1986); J. Comput. Phys. 97 (1991) 566; N.Z. Akopov, G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, J. Comput. Phys. 97 (1991) 573. [30] M. Lüscher, Comput. Phys. Commun. 79 (1994) 100; F. James, Comput. Phys. Commun. 79 (1994) 111; 97 (1996) 357 (E).
51. [29] G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, EPI-865-16-86 (1986); J. Comput. Phys. 97 (1991) 566; N.Z. Akopov, G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, J. Comput. Phys. 97 (1991) 573. [30] M. Lüscher, Comput. Phys. Commun. 79 (1994) 100; F. James, Comput. Phys. Commun. 79 (1994) 111; 97 (1996) 357 (E).
52. [29] G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, EPI-865-16-86 (1986); J. Comput. Phys. 97 (1991) 566; N.Z. Akopov, G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, J. Comput. Phys. 97 (1991) 573. [30] M. Lüscher, Comput. Phys. Commun. 79 (1994) 100; F. James, Comput. Phys. Commun. 79 (1994) 111; 97 (1996) 357 (E).
53. [29] G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, EPI-865-16-86 (1986); J. Comput. Phys. 97 (1991) 566; N.Z. Akopov, G.K. Savvidy and N.G. Ter-Arutyunyan Savvidy, J. Comput. Phys. 97 (1991) 573. [30] M. Lüscher, Comput. Phys. Commun. 79 (1994) 100; F. James, Comput. Phys. Commun. 79 (1994) 111; 97 (1996) 357 (E).
54. [31] A. Savitsky and M.J.E. Golay, Anal. Chem. 36 (1964) 1627; W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C, second edition (Cambridge Univ. Press, Cambridge).
55. [31] A. Savitsky and M.J.E. Golay, Anal. Chem. 36 (1964) 1627; W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C, second edition (Cambridge Univ. Press, Cambridge).