Bulk Q-cocycles determine renormalized and anomaly Q-cocycles on asymptotic boundaries of gauge PDEs, with the anomaly structure reproducing the holographic Weyl anomaly in AdS.
The ambient metric
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is established. Definitions and properties of conformal curvature tensors defined by ambient metrics together with formulation and proof of a jet isomorphism theorem with application to the characterization of scalar conformal invariants are given.
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Gravitational radiation at null infinity is characterized via asymptotic super-momentum properties for any cosmological constant, matching the news tensor when Lambda equals zero and providing a reliable definition otherwise.
Recovers Minkowski massless integer-spin solution space as smooth limit of AdS solution space for even dimensions via cosmological-constant expansion of source and vev.
Positivity of a weighted holographic energy is proven for 4D spacetimes with negative cosmological constant and conformally static boundaries of spherical or toroidal topology with compatible spin structure.
A relative holographic energy coincides with the relative Hamiltonian energy.
The paper derives the Schwarzian derivative in AdS2/CFT1 from boundary extrinsic curvature and the Cotton tensor in AdS4/CFT3 from a boundary gravitational Chern-Simons term, both as remnants of broken conformal gauge symmetry.
citing papers explorer
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Asymptotic boundary structure of Lagrangian gauge theories
Bulk Q-cocycles determine renormalized and anomaly Q-cocycles on asymptotic boundaries of gauge PDEs, with the anomaly structure reproducing the holographic Weyl anomaly in AdS.
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Characterization of gravitational radiation at infinity with a cosmological constant
Gravitational radiation at null infinity is characterized via asymptotic super-momentum properties for any cosmological constant, matching the news tensor when Lambda equals zero and providing a reliable definition otherwise.
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Flat from AdS: in any dimension and for any spin
Recovers Minkowski massless integer-spin solution space as smooth limit of AdS solution space for even dimensions via cosmological-constant expansion of source and vev.
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Positivity of holographic energy
Positivity of a weighted holographic energy is proven for 4D spacetimes with negative cosmological constant and conformally static boundaries of spherical or toroidal topology with compatible spin structure.
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Holographic is Hamiltonian, relatively
A relative holographic energy coincides with the relative Hamiltonian energy.
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Gauge Theory of Gravity and the AdS/CFT Correspondence
The paper derives the Schwarzian derivative in AdS2/CFT1 from boundary extrinsic curvature and the Cotton tensor in AdS4/CFT3 from a boundary gravitational Chern-Simons term, both as remnants of broken conformal gauge symmetry.