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arXiv 1303.6955hep-th
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大中心荷下的纠缠熵

Entanglement Entropy at Large Central Charge

Thomas Hartman

摘要:

利用共形块展开研究了具有大中心荷和少量低维算子的二维共形场论。推导出了基态N个不相交区间的Renyi熵的通用公式,该公式适用于级数展开中的所有阶次。这是可能的,因为在这个区域中,完全微扰的答案来自于应力张量和真空态的其他后代的交换。因此,Renyi熵与大中心荷下的Virasoro真空块有关。通过解析延拓从Renyi熵计算出的纠缠熵,可以叠加成单区间纠缠的总和。这一场论结果与Ryu-Takayanagi公式的全息纠缠熵的二维CFT,适用于任何数量的间隔,因此可以解释为微观计算的面积最小的表面在三维重力。

英文摘要:

Two-dimensional conformal field theories with a large central charge and a small number of low-dimension operators are studied using the conformal block expansion. A universal formula is derived for the Renyi entropies of N disjoint intervals in the ground state, valid to all orders in a series expansion. This is possible because the full perturbative answer in this regime comes from the exchange of the stress tensor and other descendants of the vacuum state. Therefore, the Renyi entropy is related to the Virasoro vacuum block at large central charge. The entanglement entropy, computed from the Renyi entropy by an analytic continuation, decouples into a sum of single-interval entanglements. This field theory result agrees with the Ryu-Takayanagi formula for the holographic entanglement entropy of a 2d CFT, applied to any number of intervals, and thus can be interpreted as a microscopic calculation of the area of minimal surfaces in 3d gravity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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