广义复杂度与全息Vaidya时空中的动力学响应
Generalized complexity and dynamical response in holographic Vaidya spacetimes
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中文总结 AI 辅助
本研究通过数值分析和FG展开，证明全息Vaidya时空的广义复杂度在淬火中由边界应力张量及其导数控制，并建立其与线性响应谱密度的联系。
中文摘要 AI 辅助
我们研究了光滑Vaidya几何中的“Complexity=Anything”猜想，采用Weyl平方泛函作为我们研究中最常见的候选方案。我们在4维和5维Reissner-Nordström（RN）以及5维Gauss-Bonnet（GB）背景下对候选方案进行的数值分析显示，其演化同时依赖于$r$和$v$（“双重复杂度”），这与仅依赖于$r$的静态解不同。随后，我们利用Fefferman-Graham展开研究了渐近AdS区域中静态解与动力学解复杂度之间的差异。通过同时展开体度规、极值嵌入、诱导度规、法向量和外曲率，我们证明了前四个FG系数在两个几何之间相互抵消。相反，第一个非零贡献出现在第五个系数处，并由边界应力张量及其导数控制。在Vaidya淬火过程中，导数贡献编码了边界态的时间依赖响应。在线性响应中，该响应由延迟应力张量关联函数支配，并通过广义Kramers-Kronig关系，可以用其谱密度来表示。因此，我们确定了广义全息复杂度与动力学应力张量响应之间的联系，在线性响应区域中，该响应可以用相应的应力张量谱密度来表示。
英文摘要
We investigate "Complexity=Anything" for smooth Vaidya geometries, using the Weyl squared functional as the most common candidate for our study. Our numerical analysis of candidates in 4- and 5-dimensional Reissner-Nordström (RN) and 5-dimensional Gauss-Bonnet (GB) shows evolution in both $r$ and $v$ ("doubled complexity"), unlike static solutions that depend only on $r$. We then study the difference between the complexity of static and dynamical solutions in the asymptotically AdS regime using a Fefferman-Graham expansion. By expanding the bulk metric, extremal embedding, induced metric, normal vector, and extrinsic curvature simultaneously, we show that the first four FG coefficients cancel between the two geometries. In contrast, the first nonvanishing contribution occurs at the fifth coefficient and is controlled by the boundary stress tensor and its derivatives. During the Vaidya quench, the derivative contribution encodes the time-dependent response of the boundary state. In linear response, this response is governed by the retarded stress-tensor correlator and, through generalized Kramers-Kronig relations, can be represented in terms of its spectral density. We thus identify a connection between generalized holographic complexity and the dynamical stress-tensor response, which in the linear-response regime can be represented in terms of the corresponding stress-tensor spectral density.
发表机构
- Ayatollah Boroujerdi University（阿亚图拉·布鲁杰迪大学）
- Institute for Research in Fundumental Sciences (IPM)（基础科学研究院）
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