Video URL
https://pirsa.org/23090114Weyl-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. https://pirsa.org/23090114
MLA
Jia, Weizhen. Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography. Perimeter Institute for Theoretical Physics, Sep. 28, 2023, https://pirsa.org/23090114
BibTex
@misc{ scivideos_PIRSA:23090114, doi = {10.48660/23090114}, url = {https://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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