Covariant theory of asymptotic symmetries, conservation laws and central charges

By G. Barnich, Friedemann Brandt. 2001

686 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e38593f9d0e8110f3b0c32f0518baf92ce3f88e1

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In Applied Mathematics

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Citations in the corpus

Kerr-CFT and gravitational perturbations (2009, methodology): “63) Now, assuming that ξ is a Killing field of the background, a standard manipulation [28, 29, 30] based on the second-order Einstein equation (3.”
Hidden Conformal Symmetry of the Kerr Black Hole (2010, background): “In some cases, such central charges can be derived from an analysis of the asymptotic symmetry group [20,12,21,22].”
Extended symmetries at the black hole horizon (2016, methodology): “In our case, it is not necessary to introduce any constant to be ulteriorly set to the Planck scale, but our expressions for the charges smoothly follows from the covariant approach [29, 30].”
BMS charge algebra (2011, background): “In the covariant approach, one can show a similar result [10, 12] .”
Warped Conformal Field Theory (2012, background): “In the covariant formalism [80, 81, 82], the infinitesimal charge associated to an asymptotic Killing vector ζ is”
Extremal Black Hole/CFT Correspondence in (Guaged) Supergravities (2008, neutral): “φ2 ∂ ∂r . (2.12) The central charges ci in these Virasoro algebras, at the level of Dirac brackets of the associated charges Qi (n) = 1/(8π) R ∂Σ k i (n), can be calculated in the manner described in [30, 31] and applied in [1], namely from the m3 terms in the expressions 1 8π Z ∂Σ kζ i (m) [Lζ (−m)”
Kerr/CFT Correspondence (2008, background): “se conditions are obeyed around NHEK in appendix B. The charges that generate ∂τ and ζǫ are Q∂τ = 1 8πG Z ∂Σ k∂τ , Qζǫ = 1 8πG Z ∂Σ kζǫ. (6.4) 8We choose the arbitrary additive constants appearing in [34, 35] so that Q ζ[¯ g] = 0 for ¯ the NHEK metric. 9 Choosing gµν to be the NHEK background, the i”
Aspects of the BMS/CFT correspondence (2010, methodology): “In addition, the covariant expression for the surface charg es used above coincides onshell with those of the Hamiltonian formalism [56, 57].”
Black holes and asymptotics of 2 + 1 gravity coupled to a scalar field (2002, methodology): “onsistent with the modiﬁed asymptotic behavior (2.3), this conﬁguration corresponds to the ground state. A similar expression for Q(ξ) could also be found using covariant methods as, for instance, in [10]. It should be emphasized that the algebra of the charges (2.6) is identical to the one found in”
Near Extremal Kerr Entropy from AdS(2) Quantum Gravity (2009, background): “K) [4] is represented as a warped U(1) ﬁbration over AdS 2. The L Virasoro algebra emerges from the diﬀeomorphisms acting non-trivially on the asymptotic space of the near horizon geometry, following [5,6,7,8,9]. In this construction only a U(1) subgroup of the Virasoro algebra commutes with the SL(”
CFT Duals for Extreme Black Holes (2008, methodology): “To compute the charges associated with asymptotic symmetries, we use the formalism of [12,13].”
New boundary conditions for AdS3 (2013, methodology): “The asymptotic charges and asymptotic symmetry algebra can be obtained using the formalism of [36, 37, 40, 41].”
Surface charge algebra in gauge theories and thermodynamic integrability (2007, methodology): “rst order, Ri f = R i αf α + Riµ α ∂ µf α, the weakly vanishing Noether current reduces to S f = Riµ α f α δL δφi (dn−1x) µ. (3.4) 3.2 Surface charge 1-forms Motivated by the cohomological results of [38] summarized in the introduction, we consider the (n−2,1) forms 2 k f[d V φ] = In−1 d V φ S f, (3”
Chiral gravity, log gravity, and extremal CFT (2009, methodology): “Our expression follows from the covariant formalism [37, 38], which is based on [39] and has been developed in great detail for a wide variety of applications in [40].”