标题： 德西特视界熵来自简单洛伦兹路径积分 显示英文标题

标题： De Sitter horizon entropy from a simplicial Lorentzian path integral

摘要： 量子引力系统的希尔伯特空间的维度可以形式地写成洛伦兹度量上的路径积分配分函数。 我们在一个2+1维的单纯形迷你超空间模型中实现了这一点，其中系统是一个空间拓扑圆盘，并通过欧几里得鞍点的围线变形恢复了德西特静态区域的熵，除离散化误差外。 该模型说明了对正负时间间隔进行积分以强制引力约束的重要性，以及限制到使涨落积分收敛的复数度量的重要性。 尽管严格意义上的洛伦兹路径积分是振荡的，但由于作用量不可避免的虚部贡献，导致配分函数呈指数级增长。 这些贡献来自于具有二维简并的单纯形配置的作用量解析延拓，此时度量不再为洛伦兹型。 特别是，主要贡献来自于环绕圆盘边界收缩的闭合类时曲线的配置，这与最近的连续体结果密切相关。 显示英文摘要

摘要： The dimension of the Hilbert space of a quantum gravitational system can be written formally as a path integral partition function over Lorentzian metrics. We implement this in a 2+1 dimensional simplicial minisuperspace model in which the system is a spatial topological disc, and recover by contour deformation through a Euclidean saddle the entropy of the de Sitter static patch, up to discretization artifacts. The model illustrates the importance of integration over both positive and negative lapse to enforce the gravitational constraints, and of restriction to complex metrics for which the fluctuation integrals would converge. Although a strictly Lorentzian path integral is oscillatory, an exponentially large partition function results from unavoidable imaginary contributions to the action. These arise from analytic continuation of the simplicial (Regge) action for configurations with codimension-2 simplices where the metric fails to be Lorentzian. In particular, the dominant contribution comes from configurations with contractible closed timelike curves that encircle the boundary of the disc, in close correspondence with recent continuum results.