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arXiv 2409.04657hep-thgr-qc
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探索全息宇宙:纠缠熵修正的若干方面

Probing the Holographic Universe: Aspects of Entanglement Entropy Modifications

Felipe Diaz

AI总结:

本论文通过三个场景研究能量涨落和加速度对纠缠熵的影响,包括德西特时空Rindler观测者纠缠、全局U(1)对称场论的全息纠缠熵扩展及三维加速黑洞,发现加速度导致信息丢失。

摘要:

纠缠熵对于理解量子力学与信息论之间的联系至关重要。本论文通过三个关键场景研究能量涨落和加速度如何影响纠缠熵。首先,我们分析了德西特时空中不相交的Rindler观测者之间的纠缠。我们引入共形场论配分函数的单圈修正,这打破了先前平坦的纠缠谱,并导致纠缠熵的面积律,同时保持了希尔伯特空间的有限性。其次,我们将全息纠缠熵框架扩展到具有全局$U(1)$对称性的场论,考虑非线性带电理论及其热涨落和量子涨落。我们发现,对偶理论经历自发对称破缺,并且由于量子修正,$\langle TT\rangle$关联函数的前导阶系数减小。以共形电动力学与三维引力耦合为例,我们探索了一个黑洞解及其与二维自由玻色子的联系。最后,我们研究了三维加速黑洞,揭示出加速度的增加会减少可到达的边界区域,从而减少纠缠熵。这表明加速度导致对偶理论中的信息丢失。

英文摘要:

Entanglement entropy is crucial for understanding the link between quantum mechanics and information theory. This thesis investigates how energy fluctuations and acceleration affect entanglement entropy through three key scenarios. First, we analyze entanglement between disjoint Rindler observers in de Sitter spacetime. We introduce 1-loop corrections to the partition function of the conformal field theory, disrupting the previously flat entanglement spectrum and resulting in an area law for entanglement entropy, while preserving the finiteness of the Hilbert space. Next, we extend the holographic entanglement entropy framework to field theories with global $U(1)$ symmetry, considering non-linearly charged theories and their thermal and quantum fluctuations. We find that the dual theory experiences spontaneous symmetry breaking and a reduction in the leading-order coefficient of the $\langle TT\rangle$ correlator due to quantum corrections. Using conformal electrodynamics coupled with three-dimensional gravity as an example, we explore a black hole solution and its connection to two-dimensional free bosons. Finally, we investigate three-dimensional accelerating black holes, revealing that increased acceleration reduces the accessible boundary region and, consequently, the entanglement entropy. This suggests a loss of information in the dual theory due to acceleration.

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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