二维共形场论中 Page 型熵偏移的尖锐零能量下界
Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory
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- Ibn Tofail University（伊本·图费利大学）
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中文总结 AI 辅助
本研究在二维共形场论中推导了 Page 型熵偏移能量代价的尖锐下界，确定了最小化能量所需的熵分布，并给出了总正能量有限的更强必要条件。
中文摘要 AI 辅助
我们在二维共形场论中推导了 Page 型纠缠熵偏移的能量代价的尖锐下界。对于满足初级量子零能量条件（QNEC）的状态，正零能量 \\(E_+\\) 满足一个尖锐下界，该下界由阈值 \\(\Delta S=(c/6)\ln 2\\) 分为两支。我们还推导了净能量 \\(E_{\rm net}\\) 的尖锐下界，其系数比 Abdolrahimi 和 Page [Phys. Rev. D 92, 083005 (2015)] 给出的值大两倍，并且在 QNEC 饱和扇区中，我们获得了负能量 \\(E_-\\) 的尖锐下界。这些常数作为光滑共形真空上的下确界是尖锐的。我们确定了对于一般 QNEC 状态使 \\(E_+\\) 最小化的熵分布，以及在饱和扇区中使 \\(E_-\\) 最小化的熵分布。最后，对于在有限时间内包含无限序列的小子偏移的偏移，我们推导了总正能量保持有限的一个必要条件，该条件比要求熵具有有限总变差更强。
英文摘要
We derive sharp lower bounds on the energy cost of Page-like entanglement entropy excursions in two-dimensional conformal field theory. For states satisfying the primary quantum null energy condition (QNEC), the positive null energy \(E_+\) obeys a sharp lower bound with two branches separated by the threshold \(ΔS=(c/6)\ln 2\). We also derive a sharp lower bound on the net energy \(E_{\rm net}\), with a coefficient larger by a factor of two than the value quoted by Abdolrahimi and Page [Phys. Rev. D 92, 083005 (2015)] and, in the QNEC-saturating sector, we obtain a sharp lower bound on the negative energy \(E_-\). The constants are sharp as infima over smooth conformal vacua. We determine the entropy profiles that minimize \(E_+\) for general QNEC states and the one that minimizes \(E_-\) in the saturating sector. Finally, for an excursion containing an infinite sequence of small sub-excursions within a finite duration, we derive a necessary condition for the total positive energy to remain finite, which is stronger than requiring the entropy to have finite total variation.
