SIGMA 2 (2006), 086, 5 pages      hep-th/0610194      https://doi.org/10.3842/SIGMA.2006.086
Contribution to the Proceedings of the O'Raifeartaigh Symposium

Quantum Gravity as a Broken Symmetry Phase of a BF Theory

Aleksandar Miković ^{a, b
a)} Department of Mathematics, Lusofona University, Av. Do Campo Grande 376, 1749-024 Lisbon, Portugal
^b) Mathematical Physics Group, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisbon, Portugal

Received October 02, 2006, in final form November 21, 2006; Published online December 07, 2006

Abstract
We explain how General Relativity with a cosmological constant arises as a broken symmetry phase of a BF theory. In particular we show how to treat de Sitter and anti-de Sitter cases simultaneously. This is then used to formulate a quantisation of General Relativity through a spin foam perturbation theory. We then briefly discuss how to calculate the effective action in this quantization procedure.

Key words: de Sitter; anti-de Sitter; spin foams.

pdf (171 kb)   ps (138 kb)   tex (9 kb)

References

1. Green M.B., Schwarz J.H., Witten E., Superstring theory, Vols. 1, 2, Cambridge University Press, 1987.
2. Rovelli C., Loop quantum gravity, Living Rev. Relativ., 1998, V.1, 1998-1, 68 pages, gr-qc/9710008.
3. Baez J.C., An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics (1999, Schladming), Lecture Notes in Phys., Vol. 543, Berlin, Springer, 2000, 25-93, gr-qc/9905087.
4. Crane L., Kauffman L.H., Yetter D., State-sum invariants of 4-manifolds, J. Knot Theory Ramifications, 1997, V.6, 177-234, hep-th/9409167.
5. Barrett J.W., Crane L., Relativistic spin networks and quantum gravity, J. Math. Phys., 1998, V.39, 3296-3302, gr-qc/9709028.
6. Barrett J.W., Crane L., A Lorentzian signature model for quantum general relativity, Classical Quantum Gravity, 2000, V.17, 3101-3118, gr-qc/9904025.
7. Crane L., Perez A., Rovelli C., Perturbative finiteness in spin-foam quantum gravity, Phys. Rev. Lett., 2001, V.87, 181301, 4 pages.
8. Baez J.C., Christensen J.D., Halford T.R., Tsang D.C., Spin foam models of Riemannian quantum gravity, Classical Quantum Gravity, 2002, V.19, 4627-4648, gr-qc/0202017.
9. MacDowell S.W., Mansouri F., Unified geometric theory of gravity and supergravity, Phys. Rev. Lett., 1977, V.38, 739-742.
10. Smolin L., Starodubtsev A., General relativity with a topological phase: an action principle, hep-th/0311163.
11. Miković A., Quantum gravity as a deformed topological quantum field theory, J. Phys. Conf. Ser., 2006, V.33, 266-270, gr-qc/0511077.
12. Freidel L., Louapre D., Diffeomorphisms and spin foam models, Nuclear Phys. B, 2003, V.662, 279-298, gr-qc/0212001.
13. Freidel L., Louapre D., Ponzano-Regge model revisited. I. Gauge fixing, observables and interacting spinning particles, Classical Quantum Gravity, 2004, V.21, 5685-5726, hep-th/0401076.