PIRSA:23090114

Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography

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

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

          @misc{ pirsa_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},
            year = {2023},
            month = {sep},
            note = {PIRSA:23090114 see, \url{https://pirsa.org}}
          }

Weizhen Jia

University of Illinois Urbana-Champaign

Talk number
PIRSA:23090114
Collection
Talk Type
Subject
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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Zoom link https://pitp.zoom.us/j/91781363979?pwd=NlhjTVlHTlhMSTcxYnk5eExkTWFqdz09