Boundary actions in Ponzano-Regge discretization, quantum groups and AdS3

Advances in Theoretical and Mathematical Physics

Volumn 6, Issue 5, 2002, Pages 795-826

  O'Loughlin, Martin ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

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EID: 21244498378     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/ATMP.2002.v6.n5.a1     Document Type: Article

References (66)

1. M. Blau and G. Thompson, "A new class of topological field theories and Ray-Singer torsion," Phys.Lett. B228 (1989), 64.
2. "Topological Gauge Theories of antisymmetric tensor fields", Ann. Phys. 205 (1991), 130.
3. G. Horowitz, "Exactly soluble diffeomporphism invariant theories", Commun. Math. Phys. 125 (1989) 417.
4. S. Elitzur, G. Moore, A. Schwimmer and N. Seiberg, "Remarks on the canonical quantization of the Chern-Simons-Witten theory." Nucl. Phys. B326 (1989) 108.
5. G. Ponzano and T. Regge, "Semi-classical Limit of Racah Coefficients," in Spectroscopic and Group theoretical Methods in Physics p.1, ed. F. Bloch, (North-Holland, 1968).
6. E. Witten, "(2 + 1)-dimensional gravity as an exactly soluble system", Nucl. Phys. B311 (1988) 46.
7. G. 't Hooft, "Quantization of point particles in (2 + 1)-dimensional gravity and space-time discreteness", Class. Quant. Grav. 13 (1996) 1023.
8. G. 't Hooft, "Dimensional reduction in quantum gravity".
9. L. Susskind, "The World as a Hologram".
10. G. 't Hooft, Nucl. Phys. 256 (1985), 727.
11. G. 't Hooft, Nucl. Phys. B335 (1990) 138.
12. G. 't Hooft, Phys. Scr. T36 (1991) 247.
13. L. Susskind, L. Thorlacius and J. Uglum, Phys. Rev. D48 (1993) 3743.
14. L. Freidel and K. Krasnov, "Spin foam models and the classical action principle".
15. N.Kawamoto, H.B. Nielsen and N Sato, "Lattice Chern-Simons gravity via Ponzano-Regge Model".
16. S. Chung, M. Fukuma and A. Shapere, "Structure of topological lattice theories in three dimensions".
17. M. Reisenberger, "A left-handed action for Euclidean general relativity.", Class. Quant. Grav. 14 (1997), 1753.
18. D.A. Varshalovich, A.N. Moskalev and V.K. Khersonskii, "Quantum Theory of Angular Momentum". Singapore: World Scientific, 1988.
19. T. Regge, Nuovo Cimento 19 (1961) 551.
20. U. Pachner, "Shellings of simplicial balls and p.l. manifolds with boundary," Discr. Math. 81 (1990), 37.
21. "P.L homeomorphic manifolds are equivalent by elementary shellings," Europ. J. Combinatorics 12 (1991), 129.
22. V.G. Turaev and O. Ya. Viro, "State sum invariants of 3-manifolds and quantum 6j-symbols," Topology31 (1992), 865.
23. S. Mizoguchi and T. Tada, "3-dimensional gravity from the Turaev-Viro invariant".
24. F.A. Bais and N.M. Muller, "Topological field theory and the quantum double of SU(2)".
25. H. Ooguri, "Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano-Regge," Nucl. Phys. B382 (1992) 276.
26. H. Ooguri and N.Sasakura, "Discrete and continuum approaches to three-dimensional quantum gravity," Mod. Phys. Lett. A6 (1991) 3591.
27. M. Blau, I. Jermyn and G. Thompson, "Solving topological field theories on Mapping Tori," Phys. Lett. B383 (1996) 169.
28. J.D. Brown and M. Henneaux, "Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity." Comm. Math. Phys. 104(1986), 207.
29. O. Coussaert, M. Henneaux and P. van Driel, "The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant".
30. J. Ambjørn and R. Loll, "Non-perturbative Lorentzian Quantum gravity, causality and topology change".
31. J. Ambjørn, J. Jurkiewicz and R. Loll, "A non-perturbative Lorentzian path-integral for gravity".
32. J. Ambjørn, J. Jurkiewicz and R. Loll, "Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results".
33. C. Bachas and P.M.S. Petropoulos, Comm. Math. Phys. 152 (1993), 191.
34. M. Fukuma, S. Hosono and H. Kawai, "Lattice topological field theory in two-dimensions".
35. G. Carbone, M. Carfora and A. Marzuoli, "Wigner symbols and combinatorial invariants of three-manifolds with boundary," DFNT-T 14/98, SISSA 118/98/FM, "Invariants of spin networks with boundary in quantum gravity and TQFT".
36. J. Maldacena, "The large N limit of superconformal field theories and supergravity", Adv. Theor. Math. Phys. 2 (1998) 231.
37. S. Gubser, I. Klebanov and A. Polyakov, "Gauge theory correlators from noncritical string theory", Phys. Lett. B428 (1998) 105.
38. E. Witten, "Anti de Sitter space and holography", Adv. Theor. Math. Phys. 2 (1998) 2253.
39. J.W. Barrett and T.J. Foxon, "Semi-classical limits of simplicial quantum gravity".
40. S. Davids, "Semiclassical Limits of Extended Racah coefficients".
41. D. Gross and A. Migdal, Phys. Rev. Lett. 64 (1990) 127.
42. T. Banks, M. Douglas, N. Seiberg and S. Shenker, Phys. Lett. B238 (1990) 279.
43. G. Moore, N. Seiberg and M. Staudacher, Nucl. Phys. B362 (1991) 665.
44. G. 't Hooft, "Transplanckian particles and the quantization of time", Class. Quant. Grav. 16 (1999), 395.
45. A. Ashtekar, J. Baez, A. Corichi and K. Krasnov "Quantum Geometry and Black Hole Entropy," Phys. Rev. Lett. 80 (1998) 904.
46. V. Suneeta, R.K. Kaul and T.R. Govindarajan, "BTZ Black hole entropy from Ponzano-Regge gravity".
47. H. Dorn and H.-J. Otto, "Two and three-point functions in Liouville theory".
48. A.B. Zamolodchikov and Al.B. Zamolodchikov, "Structure Constants and conformal bootstrap in Liouville field theory".
49. B. Ponsot and J. Teschner, "Liouville Bootstrap via harmonic analysis on a non-compact quantum group".
50. 3", Adv. Theor. Math. Phys. 2 (1998) 733.
51. J. Maldacena and H. Ooguri, "Strings in ADS(3) and SL(2, R) WZW model".
52. A. Kato and Y. Satoh, "Modular invariance of string theory on AdS(3)".
53. G. Arcioni, S. de Haro and M. O'Loughlin, work in progress.
54. H. Steinacker, "Quantum Anti-de Sitter space and sphere at roots of unity.".
55. A. Jevicki and S. Ramgoolam, "Non-commutative gravity from the ADS/CFT correspondence" JHEP 9904 (1999) 32.
56. S. Randjbar-Daemi and D. Jatkar, "Type IIB string theory on AdS5 × Tnn′", Phys.Lett. B460 (1999) 281.
57. L.D. Fadeev and O. Tirkkonen, "Connections of the Liouville Model and the XXZ spin chain," Nucl. Phys. B453 (1995) 647.
58. G. 't Hooft, "Quantum Gravity as a Dissipative deterministic system", Class.Quant.Grav. 16 (1999) 3263.
59. "Black Holes: The Membrane Paradigm" eds. K.S. Thorne, R.H. Price and D.A. MacDonald, (Yale University Press, London, 1986).
60. M.K. Parikh and F. Wilczek, "An action for Black Hole Membranes", Phys.Rev. D58 (1998), 064011.
61. J.W. Barrett and L. Crane, "Relativistic spin networks and quantum gravity", J. Math. Phys. 39 (1998) 3296.
62. J.W. Barrett and L. Crane, "A Lorentzian signature model for quantum general relativity".
63. J.W. Barrett and R.M. Williams, "The asymptotics of an amplitude for the four-simplex".
64. M. Reisenberger and C. Rovelli, "Sum over surfaces formulation of loop quantum gravity", Phys.Rev. D56 (1997), 3490.
65. M. Reisenberger, "A lattice world-sheet sum for 4-d Euclidean general relativity".
66. J. Barrett and L. Crane, "Relativistic spin networks and quantum gravity", J. Math. Phys. 39 (1998) 3296.