Title: Weyl-Ambient Metrics, Obstruction Tensors and Their Roles in Holography
Speaker: Weizhen Jia（贾唯真）
Affiliation: University of Wurzburg, Germany（德国维尔茨堡大学）
Time: 14:00-15:00, Friday, 25th October, 2024 (UTC+8, Beijing Time)
Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Inviter: Zhijin Li （李志金）
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.
Speaker
Dr. Weizhen Jia is currently a postdoc at the University of Wurzburg, Germany.