Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. The commonly used Fefferman-Graham gauge for asymptotically locally AdS spacetimes explicitly breaks the Weyl symmetry of the boundary theory. This can be resolved by applying the Weyl-Fefferman-Graham (WFG) gauge, in which the boundary carries a Weyl geometry. We generalize the Fefferman-Graham ambient construction for conformal geometry to a corresponding construction for 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 in the WFG gauge, we demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory. Furthermore, the holographic calculation with a background Weyl geometry also implies an underlying geometric interpretation of the Weyl anomaly.

报告人简介

贾唯真，2017年本科毕业于北京师范大学，2024年博士毕业于美国伊利诺伊大学厄巴纳香槟分校(UIUC)，目前为德国维尔茨堡大学博士后，研究方向包括高能理论、凝聚态理论和数学物理，主要从事量子场论、全息对偶、量子反常以及拓扑相的相关研究。

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吴洁强 副研究员