A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant

Glenn Barnich; Andrés Gomberoff; Hernán A. González

doi:10.1007/978-3-642-40157-2_11

A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant

Glenn Barnich, Andrés Gomberoff, Hernán A. González

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS₃ invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.

Original language	English
Title of host publication	Progress in Mathematical Relativity, Gravitation and Cosmology - Proceedings of the Spanish Relativity Meeting ERE2012
Publisher	Springer New York LLC
Pages	135-138
Number of pages	4
ISBN (Print)	9783642401565
DOIs	https://doi.org/10.1007/978-3-642-40157-2_11
State	Published - 2014
Externally published	Yes
Event	Spanish Relativity Meeting, ERE 2012 - Guimaraes, Portugal Duration: 3 Sep 2012 → 7 Sep 2012

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	60
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Spanish Relativity Meeting, ERE 2012
Country/Territory	Portugal
City	Guimaraes
Period	3/09/12 → 7/09/12

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10.1007/978-3-642-40157-2_11

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Barnich, G., Gomberoff, A., & González, H. A. (2014). A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant. In Progress in Mathematical Relativity, Gravitation and Cosmology - Proceedings of the Spanish Relativity Meeting ERE2012 (pp. 135-138). (Springer Proceedings in Mathematics and Statistics; Vol. 60). Springer New York LLC. https://doi.org/10.1007/978-3-642-40157-2_11

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title = "A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant",

abstract = "In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS3 invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.",

author = "Glenn Barnich and Andr{\'e}s Gomberoff and Gonz{\'a}lez, {Hern{\'a}n A.}",

year = "2014",

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language = "English",

isbn = "9783642401565",

series = "Springer Proceedings in Mathematics and Statistics",

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Barnich, G, Gomberoff, A & González, HA 2014, A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant. in Progress in Mathematical Relativity, Gravitation and Cosmology - Proceedings of the Spanish Relativity Meeting ERE2012. Springer Proceedings in Mathematics and Statistics, vol. 60, Springer New York LLC, pp. 135-138, Spanish Relativity Meeting, ERE 2012, Guimaraes, Portugal, 3/09/12. https://doi.org/10.1007/978-3-642-40157-2_11

A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant. / Barnich, Glenn; Gomberoff, Andrés; González, Hernán A.

Progress in Mathematical Relativity, Gravitation and Cosmology - Proceedings of the Spanish Relativity Meeting ERE2012. Springer New York LLC, 2014. p. 135-138 (Springer Proceedings in Mathematics and Statistics; Vol. 60).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS3 invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.

AB - In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS3 invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.

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BT - Progress in Mathematical Relativity, Gravitation and Cosmology - Proceedings of the Spanish Relativity Meeting ERE2012

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A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant

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