Generalised Chern-Simons actions for 3d gravity and κ-Poincaré symmetry

Nuclear Physics B

Volumn 806, Issue 3, 2009, Pages 462-488

  Meusburger, C ^a   Schroers, B J ^b  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53249083952     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2008.06.023     Document Type: Article

References (33)

1. Lukierski J., Nowicki A., Ruegg H., and Tolstoi V. q-deformation of Poincaré algebra. Phys. Lett. B 264 (1991) 331-338
2. Lukierski J., Nowicki A., and Ruegg H. New quantum Poincaré algebra and κ-deformed field theory. Phys. Lett. B 293 (1992) 344-352
3. Majid S., and Ruegg H. Bicrossproduct structure of the κ-Poincaré group and non-commutative geometry. Phys. Lett. B 334 (1994) 348
4. Amelino-Camelia G., Smolin L., and Starodubtsev A. Quantum symmetry, the cosmological constant and Planck scale phenomenology. Class. Quantum Grav. 21 (2004) 3095-3110
5. Achucarro A., and Townsend P. A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories. Phys. Lett. B 180 (1986) 85-100
6. Witten E. 2 + 1 dimensional gravity as an exactly soluble system. Nucl. Phys. B 311 (1988) 46-78
7. Ballesteros A., Herranz F.J., Del Olmo M.A., and Santander M. Quantum (2 + 1) kinematical algebras: A global approach. J. Phys. A: Math. Gen. 27 (1994) 1283-1298
8. Ballesteros A., Bruno N.R., and Herranz F.J. Non-commutative relativistic spacetimes and wordlines from 2 + 1 quantum (anti) de Sitter groups. hep-th/0401244
9. Freidel L., Kowalski-Glikman J., and Smolin L. 2 + 1 gravity and doubly special relativity. Phys. Rev. D 69 (2004) 044001
10. Chari V., and Pressley A. A Guide to Quantum Groups (1994), Cambridge Univ. Press, Cambridge
11. Majid S. Foundations of Quantum Group Theory (1995), Cambridge Univ. Press, Cambridge
12. Kosmann-Schwarzbach Y. Lie bi-algebras, Poisson-Lie groups, and dressing transformations. Lect. Notes Phys. 638 (2004) 107-173
13. Schlieker M., Weich W., and Weixler R. Inhomogeneous quantum groups. Z. Phys. C (1992) 79-82
14. Majid S. Braided momentum in q-Poincaré group. J. Math. Phys. 34 (1993) 2045-2058
15. Zakrzewski S. Quantum Poincaré group related to κ-Poincaré algebra. J. Phys. A (1994) 2075-2082
16. Kosinski P., and Maslanka P. The duality between κ-Poincaré group algebra and κ-Poincaré group. hep-th/9411033
17. Fock V.V., and Rosly A.A. Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices. math.QA/9802054 ITEP preprint (1992) 72-92
18. Alekseev A.Yu., and Malkin A.Z. Symplectic structure of the moduli space of flat connections on a Riemann surface. Commun. Math. Phys. 169 (1995) 99-119
19. Semenov-Tian-Shansky M.A. Dressing transformations and Poisson-Lie group actions. Publ. Res. Instrum. Math. Sci. Kyoto University 21 (1986) 1237-1260
20. Buffenoir E., Noui K., and Roche P. Hamiltonian quantization of Chern-Simons theory with SL (2, C) group. Class. Quantum Grav. 19 (2002) 4953-5016
21. Meusburger C., and Schroers B.J. Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity. Class. Quantum Grav. 20 (2003) 2193-2233
22. Meusburger C., and Schroers B.J. Boundary conditions and symplectic structure in the Chern-Simons formulation of 2 + 1 dimensional gravity. Class. Quantum Grav. 22 (2005) 3689-3724
23. Meusburger C. Geometrical (2 + 1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant. Commun. Math. Phys. 273 (2007) 705
24. Bonzom V., and Livine E.R. A Immirzi-like parameter for 3d quantum gravity. arXiv: 0801.424 [gr-qc]
25. Meusburger C., and Schroers B.J. Quaternionic and Poisson-Lie structures in 3d gravity: The cosmological constant as deformation parameter. arXiv: 0708.1507 [gr-qc]
26. Meusburger C., and Schroers B.J. Phase space structure of Chern-Simons theory with a non-standard puncture. Nucl. Phys. B 738 (2006) 425-456
27. Meusburger C. Grafting and Poisson structure in (2 + 1)-gravity with vanishing cosmological constant. Commun. Math. Phys. 266 (2006) 735-775
28. Meusburger C. Dual generators of the fundamental group and the moduli space of flat connections. J. Phys. A 39 (2006) 14781-14832
29. Kowalski-Glikman J., and Nowak S. Doubly special relativity theories as different basis for κ-Poincaré algebra. Phys. Lett. B 539 (2002) 126-132
30. Bais F.A., Muller N.M., and Schroers B.J. Quantum group symmetry and particle scattering in (2 + 1)-dimensional quantum gravity. Nucl. Phys. B 640 (2002) 3-45
31. *. Adv. Theor. Math. Phys. 7 (2004) 1003-1043
32. Schroers B.J. Lessons from (2 + 1)-dimensional quantum gravity, in: Proceedings PoS (QG-Ph) 035 for workshop "From Quantum to Emergent Gravity: Theory and Phenomenology", Trieste 2007. arXiv: 0710.5844 [gr-qc]
33. Majid S., and Schroers B.J. q-deformation and semidualisation in 3d quantum gravity. arXiv: 0806.2587 [gr-qc]