Weyl-Ambient Geometries

Weizhen Jia; Manthos Karydas; Robert G. Leigh

doi:10.1016/j.nuclphysb.2023.116224

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arXiv · 2301.06628

Weyl-Ambient Geometries

Weizhen Jia·Manthos Karydas·Robert G. Leigh

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Abstract

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 top-down perspective, we show that 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 $\mathbb{R}_+$-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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hep-th gr-qc math-ph math.DG math.MP

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BibTeX RIS

Weizhen Jia, Manthos Karydas, Robert G. Leigh. 2023-01-16. Weyl-Ambient Geometries. https://doi.org/10.1016/j.nuclphysb.2023.116224

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