Holographic complexity and volume
Holographic complexity and volume
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DOI：
10.1007/jhep11(2018)044
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发表时间：
2018-07
影响因子：
5.4
通讯作者：
Josiah D. Couch;Stefan Eccles;T. Jacobson;P. Nguyen
中科院分区：
文献类型：
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作者：
Josiah D. Couch;Stefan Eccles;T. Jacobson;P. Nguyen
先前提出的“复杂性=体积”或CV对偶性在多个方向上进行了探索和发展。我们证明，如果以从地平线到“最终切片”（乘以普朗克面积）的最大时间为单位测量体积，则可以消除大黑洞和小黑洞明显缺乏普遍性的现象。这也适用于旋转黑洞。我们利用守恒的“体积电流”，它与最大体积切片的时空叶状结构相关，其通量测量其体积。该通量图表明，全息 CFT 中的复杂性从紫外线转移到红外线，这让人想起使用全息术推导出的热化行为。当应用于黑洞视界时，它也自然地给出了复杂性的第二定律。我们进一步建立了一个结果，支持这样的猜想：边界叶状结构决定了没有间隙的体积最大叶状结构，建立了最大体积的全局不等式，可用于推断增强不变背景上复杂化率的单调性，并在多重淬火、旋转黑洞和 Rindler-AdS 的设置中探测 CV 对偶性。
The previously proposed “Complexity= Volume” or CV-duality is probed and developed in several directions. We show that the apparent lack of universality for large and small black holes is removed if the volume is measured in units of the maximal time from the horizon to the “final slice”(times Planck area). This also works for spinning black holes. We make use of the conserved “volume current”, associated with a foliation of spacetime by maximal volume slices, whose flux measures their volume. This flux picture suggests that there is a transfer of the complexity from the UV to the IR in holographic CFTs, which is reminiscent of thermalization behavior deduced using holography. It also naturally gives a second law for the complexity when applied at a black hole horizon. We further establish a result supporting the conjecture that a boundary foliation determines a bulk maximal foliation without gaps, establish a global inequality on maximal volumes that can be used to deduce the monotonicity of the complexification rate on a boost-invariant background, and probe CV duality in the settings of multiple quenches, spinning black holes, and Rindler-AdS.