AI 中文总结
研究复极值曲面积分轮廓不明确问题，提出从其曲面族构建复体度规方法，并以KSW准则约束轮廓，解释类空纠缠选择实洛伦兹截面原因，明确构建范围与局限，突出KSW可允许性对实时全息复鞍点的作用。
AI 中文摘要
复极值曲面自然出现在与反德西特/共形场论（AdS/CFT）中类时子区域相关的全息可观测量以及德西特/共形场论（dS/CFT）中的全息可观测量中，但其积分轮廓通常不明确。在这项工作中，我们提出了一种从复极值曲面族构建复体度规的方法，从而生成与引力路径积分相关的候选复几何。此构建实现了复体几何如何从类时纠缠中出现，扩展了时空几何由量子纠缠编码的观点。我们用孔采维奇 - 西格尔 - 维滕（KSW）准则作为强一致性条件来约束相应轮廓。同一框架还解释了为什么类空纠缠自然选择实洛伦兹截面。在几个AdS和dS例子中，KSW条件唯一确定了所考虑类中的可允许轮廓。我们还识别出在渐近边界附近所得复几何违反KSW界的构型，揭示了该构建的范围和局限性。这些结果突出了KSW可允许性作为实时全息中复鞍点的有用组织原则。
英文摘要
Complex extremal surfaces naturally arise in holographic observables associated with timelike subregions in AdS/CFT and with holographic observables in dS/CFT, but their integration contours are generally ambiguous. In this work, we propose a method for constructing complex bulk metrics from families of complex extremal surfaces, thereby generating candidate complex geometries relevant to the gravitational path integral. This construction provides a concrete realization of how complex bulk geometry may emerge from timelike entanglement, extending the familiar idea that spacetime geometry is encoded in quantum entanglement. We use the Kontsevich--Segal--Witten (KSW) criterion as a strong consistency condition to constrain the corresponding contours. The same framework also explains why spacelike entanglement naturally selects a real Lorentzian section. In several AdS and dS examples, the KSW condition uniquely determines the admissible contour within the class considered. We also identify configurations for which the resulting complex geometry violates the KSW bound near the asymptotic boundary, revealing both the scope and the limitations of the construction. These results highlight KSW admissibility as a useful organizing principle for complex saddles in real-time holography.
CommentsReferences added, the dS figure revised
