AI 中文总结
该研究在平面BTZ黑膜和有限截断全息理论中发展PEE thread流，对比PEE选定流与法测地线bit-thread流的差异，明确有限截断纠缠的端点组织及全息max流的非唯一性。
AI 中文摘要
我们针对平面BTZ黑膜和有限截断全息理论，发展了PEE thread流。精确测地线距离核定义了源分辨的PEE thread流，其叠加构成无散度的bit-thread场。在BTZ中，边界-边界和边界-视界区域重现了纠缠轮廓和热视界通量。在有限截断下，两点PEE核是光滑的，且选择出宏观流，尽管由测地线基本thread构成，但这类流通常是非测地线的。我们将这些PEE选定的流与独立的法测地线bit-thread流进行比较，发现二者满足相同的RT瓶颈，但在边界校准、端点配对和非瓶颈结构上存在差异。所得构造明确展示了有限截断纠缠的端点组织以及全息max流的非唯一性。
英文摘要
We develop PEE thread flows for the planar BTZ black brane and finite-cutoff holography. Exact geodesic-distance kernels define source-resolved PEE thread currents whose superposition gives divergenceless bit-thread fields. In BTZ, boundary-boundary and boundary-horizon sectors reproduce the entanglement contour and thermal horizon flux. At finite cutoff, the two-point PEE kernels are smooth and select macroscopic flows that are generically non-geodesic despite being built from geodesic elementary threads. We compare these PEE-selected flows with independent normal-geodesic bit-thread flows and show that they saturate the same RT bottleneck while differing in boundary calibration, endpoint pairing and off-bottleneck structure. The resulting constructions make explicit both the endpoint organization of finite-cutoff entanglement and the nonuniqueness of holographic max flows.
Comments55 pages+5 appendices, 13 figures
