## Video URL

http://pirsa.org/23090114# Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography

### APA

Jia, W. (2023). Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography. Perimeter Institute for Theoretical Physics. http://pirsa.org/23090114

### MLA

Jia, Weizhen. Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography. Perimeter Institute for Theoretical Physics, Sep. 28, 2023, http://pirsa.org/23090114

### BibTex

@misc{ scivideos_PIRSA:23090114, doi = {}, url = {http://pirsa.org/23090114}, author = {Jia, Weizhen}, keywords = {Quantum Gravity}, language = {en}, title = {Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography}, publisher = {Perimeter Institute for Theoretical Physics}, year = {2023}, month = {sep}, note = {PIRSA:23090114 see, \url{https://scivideos.org/index.php/pirsa/23090114}} }

Weizhen Jia University of Illinois Urbana-Champaign

## 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, which is a generalization of the FG gauge for asymptotically locally AdS (AlAdS) spacetimes. Then, the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Through the Weyl-ambient construction, we investigate Weyl-covariant quantities on the Weyl manifold and define Weyl-obstruction tensors. We show that Weyl-obstruction tensors appear as poles in the Fefferman-Graham expansion of the AlAdS bulk metric for even boundary dimensions. Under holographic renormalization, we demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory.

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