边界引力子相干性的有限应力张量矩层析
Finite stress-tensor moment tomography of boundary-graviton coherences
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中文总结 AI 辅助
本文研究2+1维AdS3引力中边界引力子态的应力张量矩层析，证明N阶层析不完备而N+1阶完备，给出有限支撑态可区分性的精确阈值。
中文摘要 AI 辅助
2+1维爱因斯坦引力是一种拓扑理论，不允许存在局域体引力子。然而，具有Brown-Henneaux边界条件的$\mathrm{AdS}_3$引力确实允许存在边界引力子，这些引力子由Virasoro后代描述。生活在渐近边界上的观测者可以使用边界应力张量的有限阶矩作为这些态的探针。我们固定一个最高权模，并假设Shapovalov形式非退化。我们还假设观测者所探测的未知态具有已知的有限后代支撑，并且层间相干性是未知数据的一部分。我们发现，给定第$N\geq2$层的一个后代，阶为$N$的应力矩层析（即$N$次应力矩插入）在信息上是不完备的，而阶为$N+1$的应力矩层析在信息上是完备的。也就是说，在酉正则轨迹上，正交纯态可以具有相同的完整$N$阶记录。同样，对于精确有限窗口结果，当层数达到$L\geq2$时，$L$阶层析是不完备的，而$L+1$阶层析可以恢复每个密度矩阵块。相应的精确阈值在完整的左右理论中也成立。在存在半经典体解释的重扇区中，这些阈值说明了有限支撑边界引力子态何时首次变得可区分。
英文摘要
Einstein gravity in 2+1 dimensions is a topological theory that does not admit the existence of local bulk gravitons. However, $\mathrm{AdS}_3$ gravity with Brown-Henneaux boundary conditions does admit the existence of boundary gravitons, which are described by Virasoro descendants. An observer living on the asymptotic boundary can use finite order moments of the boundary stress tensor as a probe of these states. We fix one highest-weight module and assume that the Shapovalov forms are nondegenerate. We also assume that the unknown state the observer is probing has a known finite descendant support and that interlevel coherence is part of the unknown data. We find that, given a descendant at level $N\geq2$, stress moment tomography at order $N$ (meaning $N$ stress moment insertions) is informationally incomplete, while tomography with stress moments of order $N+1$ is informationally complete. This is to say that, on the unitary regular locus, orthogonal pure states can have the same complete order-$N$ record. Likewise, for exact finite-window result for levels through $L\geq2$, tomography of order $L$ is incomplete while tomography of order $L+1$ recovers every density-matrix block. Corresponding exact thresholds hold in the full left-right theory. In heavy sectors for which a semiclassical bulk interpretation exists, these thresholds say when finite-support boundary-graviton states first become distinguishable.
发表机构
- Department of Physics and Astronomy, University of Waterloo（物理学与天文学系，滑铁卢大学）
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