Weizhen Jia (Illinois): Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography

Dienstag, 24. Oktober 2023 14:00

Zoom Meeting: tuwien.zoom.us/j/67102039242

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. [...]