Obstruction tensors in Weyl geometry and holographic Weyl anomaly

Jia, Weizhen; Manthos, Karydas,

doi:10.1103/physrevd.104.126031

Cited by 13 publications

(25 citation statements)

References 48 publications

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“…Using the technique of dimensional regularization, the Weyl-obstruction tensors and extended Weylobstruction tensors were introduced as the poles in the on-shell metric expansion. It was also found in [26] that the holographic Weyl anomaly can be expressed in terms of extended Weyl-obstruction tensors. Although it is convenient to read off the extended Weyl-obstruction tensors from the pole of the AlAdS metric expansion, this should not be regarded as a precise definition since the pole may have an ambiguity when shifted by a finite term.…”

Section: Introductionmentioning

confidence: 94%

“…For example, one can define on M the Weyl-Riemann tensor Ri (0) jkl , Weyl-Ricci tensor R(0) ij , Weyl-Ricci scalar R(0) , etc. (See Appendix A of [26] for a review on Weyl geometry and the details of these Weyl-covariant quantities. )…”

Section: Induced Weyl Geometrymentioning

confidence: 99%

“…A very useful property of the ambient metric introduced in [29] in the context of conformal geometry is the ability to construct conformal-covariant tensors from the ambient Riemann tensor, including the (extended) obstruction tensors, which were generalized to (extended) Weyl-obstruction tensors in [26]. The Weyl-obstruction tensors on a d-dimensional Weyl manifold (M, [γ (0) , a (0) ]) were introduced in [26] as the poles of the metric expansion of γ ij in the AlAdS bulk. However, they can also be defined in a more explicit way from the Weyl-ambient space ( M , g).…”

Section: Weyl-obstruction Tensors: First Order Formalismmentioning

confidence: 99%

“…Starting from the metric (24), one can solve Ric(g) = 0 order by order (which is equivalent to solving the Einstein equations in the AlAdS bulk [26]) to find 7…”

Section: Weyl-obstruction Tensors: First Order Formalismmentioning

confidence: 99%

“…Following [25], the AlAdS bulk expansion in the WFG gauge was further investigated in [26]. Using the technique of dimensional regularization, the Weyl-obstruction tensors and extended Weylobstruction tensors were introduced as the poles in the on-shell metric expansion.…”

Section: Introductionmentioning

confidence: 99%

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Weyl-Ambient Geometries

Jia¹,

Manthos²,

Leigh³

2023

Preprint

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Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge. From a topdown perspective, we show that the the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Then, from a bottom-up perspective, we start from promoting a conformal manifold into a Weyl manifold by assigning a Weyl connection to the principal R + -bundle realizing a Weyl structure. We show that the Weyl structure admits a well-defined initial value problem, which determines the Weyl-ambient metric. Through the Weyl-ambient construction, we also investigate Weyl-covariant tensors on the Weyl manifold and define extended Weyl-obstruction tensors explicitly.

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Section: Introductionmentioning

confidence: 94%

Section: Induced Weyl Geometrymentioning

confidence: 99%

Section: Weyl-obstruction Tensors: First Order Formalismmentioning

confidence: 99%

“…Starting from the metric (24), one can solve Ric(g) = 0 order by order (which is equivalent to solving the Einstein equations in the AlAdS bulk [26]) to find 7…”

Section: Weyl-obstruction Tensors: First Order Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weyl-Ambient Geometries

Jia¹,

Manthos²,

Leigh³

2023

Preprint

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The ambient space formalism

Parisini,

Skenderis,

Withers

2024

J. High Energ. Phys.

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We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) n-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography.

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Radiation in holography

Ciambelli,

Pasterski,

Tabor

2024

J. High Energ. Phys.

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We show how to encode the radiative degrees of freedom in 4-dimensional asymptotically AdS spacetimes, using the boundary Cotton and stress tensors. Background radiation leads to a reduction of the asymptotic symmetry group, in contrast to asymptotically flat spacetimes, where a non-vanishing news tensor does not restrict the asymptotic symmetries. Null gauges, such as Λ-BMS, provide a framework for AdS spacetimes that include radiation in the flat limit. We use this to check that the flat limit of the radiative data matches the expected definition in intrinsically asymptotically flat spacetimes. We further dimensionally reduce our construction to the celestial sphere, and show how the 2-dimensional celestial currents can be extracted from the 3-dimensional boundary data.

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Obstruction tensors in Weyl geometry and holographic Weyl anomaly

Cited by 13 publications

References 48 publications

Weyl-Ambient Geometries

Weyl-Ambient Geometries

The ambient space formalism

Radiation in holography

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