Covariant theory of asymptotic symmetries, conservation laws and central charges

Glenn Barnich and Friedemann Brandt

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Submission date: 07. Dec. 2001 (revised version: September 2002)
Pages: 88
published in: Nuclear physics / B, 633 (2002) 1-2, p. 3-82 
DOI number (of the published article): 10.1016/S0550-3213(02)00251-1
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Abstract:
Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and asymptotically conserved n-2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters can be interpreted as asymptotic Killing vector fields of the background, with asymptotic behaviour determined by a new dynamical condition. A universal formula for asymptotically conserved n-2 forms in terms of the reducibility parameters is derived. Sufficient conditions for finiteness of the charges built out of the asymptotically conserved n-2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2-cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, Yang-Mills theory and Einstein gravity.