BTZ黑洞中Krylov spread复杂度的二次增长
The quadratic growth of Krylov spread complexity in the BTZ black hole
AI总结：
本研究针对BTZ黑洞，重构Krylov spread复杂度的边界构造，发现其增长偏离早期二次模式后回归渐近二次行为，为连接黑洞热力学与Krylov动力学提供了系统路径。
AI中文摘要：
除二维伸缩子引力外，捕捉全息复杂度量化的黑洞内部增长的边界量仍未知。我们对热场双态的Krylov spread复杂度的配分函数构造进行了关键分析，该构造能从半经典全息配分函数提供与维度无关的边界重构，同时为BTZ鞍点发展出当前的动力学和体构造。在可对比精确与半经典结果的双标度Sachdev-Ye-Kitaev模型中，我们证明仅在重构复杂度后取经典极限才可靠；若在单个Lanczos系数层面取该极限，会丢弃关键信息。将此构造应用于对偶Bañados-Teitelboim-Zanelli黑洞、高于Hawking-Page温度的大中心荷二维共形场论，我们发现其偏离早期二次增长，随后呈现与向渐近二次增长回归相符的行为，而非体积的晚期线性行为及标准的有限泛函复杂度=anything类行为。我们随后将该边界行为与由无穷多外在曲率不变量构成的广义复杂度=anything体对象匹配。该构造提供了从黑洞热力学到Krylov动力学的系统路径，且可自然扩展至高维全息黑洞。
英文摘要：
The boundary quantity that captures the growth of black-hole interiors quantified by holographic complexity remains unknown beyond 2d dilaton gravity. We provide a critical analysis of a partition-function construction of Krylov spread complexity for thermofield-double states that provides a dimension-independent boundary reconstruction from semiclassical holographic partition functions, while developing the present dynamical and bulk construction for the BTZ saddle. In the double-scaled Sachdev-Ye-Kitaev model, where exact and semiclassical results can be compared, we show that the classical limit is reliable only when taken after the complexity has been reconstructed; taking this limit at the level of individual Lanczos coefficients discards essential information. Applying the construction to a large-central-charge two-dimensional conformal field theory above the Hawking-Page temperature dual to a Bañados-Teitelboim-Zanelli black hole, we find an intermediate departure from early-time quadratic growth followed by behavior compatible with a return toward asymptotically quadratic growth, rather than the linear late-time behavior of the volume and the standard finite-functional complexity = anything class. We then match this boundary behavior to a generalized complexity = anything bulk object built from an infinite series of extrinsic-curvature invariants. The construction provides a systematic route from black-hole thermodynamics to Krylov dynamics and can naturally be extended to higher-dimensional holographic black holes.
