AI 中文总结
该研究在二维共形场论中通过解析延拓复制扭关联器制定类时纠缠熵及其Rényi扩展，在三维全息术中用半经典边界关联器推导复极值面处方，通过多种设置验证，揭示算符排序对复值熵虚部的影响，预测了AdS-Vaidya不同结果。
AI 中文摘要
我们通过将复制扭关联器解析延拓到时间有序、类时分离的插入，在二维共形场论中制定了类时纠缠熵及其Rényi扩展。这种场论构造为近期发展奠定基础并进行推广，适用于任意范围的时间子区域。在三维全息术中，半经典边界关联器将边界锚定的复测地线识别为相关的体鞍点，并选择长度实部最小的那个。这为所提出的复极值面处方提供了直接的边界推导，并扩展到Rényi指数\(n>1\)，我们在真空中明确构造了相应的复宇宙膜几何。我们在几个代表性设置中发展这些想法，包括局部和全局激发态以及量子算符猝灭，揭示了边界扭关联器和体复测地线计算之间的精确一致性。对于AdS-Vaidya，我们的方法预测了与早期分段测地线构造不同的结果，同时重现了场论答案。在这些例子中，算符排序唯一地确定了复值熵的虚部，其以\(c\pi/6\)为单位进行量子化，对有效因果结构敏感，但对基础动力学不敏感。
英文摘要
We formulate timelike entanglement entropy and its Rényi extension in two-dimensional conformal field theory through the analytic continuation of replica twist correlators to time-ordered, timelike-separated insertions. This field-theoretic construction grounds and generalizes recent developments, and applies to temporal subregions of arbitrary extent. Within three-dimensional holography, the semiclassical boundary correlator identifies boundary-anchored complex geodesics as the relevant bulk saddles and selects the one with the smallest real part of the length. This provides a direct boundary derivation of the proposed complex extremal surface prescription and extends to Rényi index $n>1$, for which we explicitly construct the corresponding complex cosmic brane geometry in the vacuum. We develop these ideas in several representative settings, including locally and globally excited states and quantum operator quenches, making manifest the precise agreement between boundary twist correlator and bulk complex geodesic calculations. For AdS-Vaidya, our approach predicts a different result from earlier piecewise geodesic constructions, while reproducing the field theory answer. Across these examples, the operator ordering uniquely determines the imaginary part of the complex-valued entropy, which is quantized in units of $cπ/6$ and sensitive to the effective causal structure but not to the underlying dynamics.
Comments42 pages + appendices, 5+6 figures
