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

PIRSA ID: 23090114
Series: Quantum Gravity
Event Type: Seminar
Scientific Area(s):
Quantum Gravity
End date:
  • Weizhen Jia, University of Illinois Urbana-Champaign

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.


Zoom link https://pitp.zoom.us/j/91781363979?pwd=NlhjTVlHTlhMSTcxYnk5eExkTWFqdz09