×

zbMATH — the first resource for mathematics

Chern–Simons formulation of three-dimensional gravity with torsion and nonmetricity. (English) Zbl 1109.83007
Various models of three-dimensional metric affine gravity are considered and it is shown that they can be written as Chern-Simons theories. Starting from the usual formulation of three-dimensional gravity and using a nonstandard decomposition of the Chern-Simons connection, the Mielke-Baekler model for arbitrary sign of the effective cosmological constant is recovered. The three-dimensional gravity with torsion is realized as a Chern-Simons theory. Torsionless but nonmetric gravitational models are considered as well.

MSC:
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C80 Analogues of general relativity in lower dimensions
83C45 Quantization of the gravitational field
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Deser, S.; Jackiw, R.; ’t Hooft, G., Three-dimensional Einstein gravity: dynamics of flat space, Ann. phys., 152, 220, (1984)
[2] Deser, S.; Jackiw, R., Three-dimensional cosmological gravity: dynamics of constant curvature, Ann. phys., 153, 405, (1984)
[3] Bañados, M.; Teitelboim, C.; Zanelli, J., The black hole in three-dimensional space-time, Phys. rev. lett., 69, 1849, (1992) · Zbl 0968.83514
[4] Carlip, S., What we don’t know about BTZ black hole entropy, Class. quant. grav., 15, 3609, (1998) · Zbl 0946.83030
[5] Achúcarro, A.; Townsend, P.K., A chern – simons action for three-dimensional anti-de Sitter supergravity theories, Phys. lett. B, 180, 89, (1986)
[6] Witten, E., (2+1)-dimensional gravity as an exactly soluble system, Nuclear phys. B, 311, 46, (1988) · Zbl 1258.83032
[7] Figueroa-O’Farrill, J.M.; Stanciu, S., Nonsemisimple sugawara constructions, Phys. lett. B, 327, 40, (1994)
[8] Hehl, F.W.; McCrea, J.D.; Mielke, E.W.; Ne’eman, Y., Metric affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance, Phys. rep., 258, 1, (1995)
[9] Kröner, E., The differential geometry of elementary point and line defects in bravais crystals, Internat. J. theoret. phys., 29, 1219, (1990) · Zbl 0709.53050
[10] Dunajski, M.; Mason, L.J.; Tod, P., Einstein – weyl geometry, the dkp equation and twistor theory, J. geom. phys., 37, 63, (2001) · Zbl 0990.53052
[11] Ward, R.S., Einstein – weyl spaces and \(\operatorname{SU}(\infty)\) Toda fields, Class. quant. grav., 7, L95, (1990) · Zbl 0687.53044
[12] Mielke, E.W.; Baekler, P., Topological gauge model of gravity with torsion, Phys. lett. A, 156, 399, (1991)
[13] Baekler, P.; Mielke, E.W.; Hehl, F.W., Dynamical symmetries in topological 3-D gravity with torsion, Nuovo cim. B, 107, 91, (1992)
[14] Deser, S.; Jackiw, R.; Templeton, S., Topologically massive gauge theories, Ann. phys., 140, 372, (1982), Ann. Phys. 185 (erratum) (1988 APNYA,281,409-449.2000) 406.1988 APNYA,281,409
[15] Blagojević, M.; Vasilić, M., 3D gravity with torsion as a chern – simons gauge theory, Phys. rev. D, 68, 104023, (2003)
[16] Witten, E., Quantization of chern – simons gauge theory with complex gauge group, Comm. math. phys., 137, 29, (1991) · Zbl 0717.53074
[17] Aharony, O.; Gubser, S.S.; Maldacena, J.M.; Ooguri, H.; Oz, Y., Large N field theories, string theory and gravity, Phys. rep., 323, 183, (2000) · Zbl 1368.81009
[18] Brown, J.D.; Henneaux, M., Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. math. phys., 104, 207, (1986) · Zbl 0584.53039
[19] García, A.A.; Hehl, F.W.; Heinicke, C.; Macías, A., Exact vacuum solution of a (1+2)-dimensional Poincaré gauge theory: BTZ solution with torsion, Phys. rev. D, 67, 124016, (2003)
[20] Coussaert, O.; Henneaux, M.; van Driel, P., The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant, Class. quant. grav., 12, 2961, (1995) · Zbl 0836.53052
[21] García, A.; Hehl, F.W.; Heinicke, C.; Macías, A., The cotton tensor in Riemannian spacetimes, Class. quant. grav., 21, 1099, (2004) · Zbl 1045.83051
[22] Eisenhart, L.P., Riemannian geometry, (1949), Princeton University Press Princeton, NJ · Zbl 0041.29403
[23] Deser, S.; Kay, J.H., Topologically massive supergravity, Phys. lett. B, 120, 97, (1983)
[24] Guralnik, G.; Iorio, A.; Jackiw, R.; Pi, S.Y., Dimensionally reduced gravitational chern – simons term and its kink, Ann. phys., 308, 222, (2003) · Zbl 1037.83012
[25] Cacciatori, S.L.; Caldarelli, M.M.; Klemm, D.; Mansi, D.S., More on BPS solutions of \(N = 2\), \(d = 4\) gauged supergravity, Jhep, 0407, 061, (2004)
[26] Horne, J.H.; Witten, E., Conformal gravity in three dimensions as a gauge theory, Phys. rev. lett., 62, 501, (1989)
[27] Weyl, H., Eine neue erweiterung der relativitätstheorie, Ann. phys., Surveys high energ. phys., 5, 237, (1986)
[28] Pedersen, H.; Tod, K.P., Three-dimensional einstein – weyl geometry, Adv. math., 97, 74, (1993) · Zbl 0778.53041
[29] Skagerstam, B.S.; Stern, A., Topological quantum mechanics in (2+1)-dimensions, Internat. J. modern. phys. A, 5, 1575, (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.