Abstract
It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.
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References
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Communicated by S. W. Hawking
Chercheur qualifié du Fonds National Belge de la Recherche Scientifique
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Brown, J.D., Henneaux, M. Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity. Commun.Math. Phys. 104, 207–226 (1986). https://doi.org/10.1007/BF01211590
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DOI: https://doi.org/10.1007/BF01211590