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- Published: 2023-11-25

**日期：**11月30日（周四）

**报告人：刘肖一**（UCSB）

**Abstract:**

Due to the conformal factor problem, the definition of the Euclidean gravitational path integral requires a non-trivial choice of contour. Here we examine a generalization of a recently proposed rule-of-thumb in ArXiv: 2202.11786 for selecting this contour at quadratic order about a saddle. The original proposal depended on the choice of an indefinite-signature metric on the space of perturbations, which was taken to be a DeWitt metric with parameter $\alpha =-1$. Here we explore contours defined using analogous prescriptions for $\alpha \neq -1$. We study such contours for Euclidean gravity linearized about AdS-Schwarzschild black holes with Dirichlet boundary conditions, and we compare path-integral stability of the associated saddles with thermodynamic stability of the classical spacetimes. While the contour generally depends on the choice of DeWitt parameter $\alpha$, the precise agreement between these two notions of stability found at $\alpha =-1$ continues to hold over the finite interval $(-2,-2/d)$, where $d$ is the dimension of the bulk spacetime. This provides criteria that may be useful in predicting metrics on the space of perturbations that give physically useful contours in more general settings.

http://www.itp.cas.cn/kxyj/xshd/xsbg/202311/t20231127_6937852.html