三维引力中的克雷洛夫复杂度与黑洞内部的增长
Krylov complexity and the growth of the black hole interior in 3D gravity
浏览论文内容
中文总结 AI 辅助
该研究从边界理论探究三维引力中黑洞内部的增长，通过关联函数重构、威尔逊线表示等方法，发现算符克雷洛夫复杂度可重现黑洞内部后期线性增长，凸显其在编码黑洞内部增长中的特殊作用及与态克雷洛夫复杂度的区别。
中文摘要 AI 辅助
我们从边界理论出发研究三维引力中黑洞内部的增长。针对双侧BTZ黑洞，我们提出利用热场双态中弥散算符的关联函数对余维一曲面的时间依赖性进行边界重构，重现了复杂度-体积提议所预言的特征后期线性增长。借助三维引力的陈-西蒙斯形式，这些非局域关联函数由带有弥散端点的体威尔逊线表示，将全息纠缠熵所基于的威尔逊线与余维二可观测量的熟悉关联扩展至余维一可观测量。随后我们探究克雷洛夫复杂度是否能捕捉到相同的几何增长。对于弥散算符，我们从其关联函数中提取兰索斯数据，发现算符克雷洛夫复杂度重现了黑洞内部的后期线性增长，将算符增长与体几何之间的先前关联扩展至AdS₃。相比之下，从半经典引力配分函数得到的热场双态的克雷洛夫扩展复杂度，在我们分析可及的范围内并未表现出体体积的线性增长。因此，我们的结果表明，算符克雷洛夫在编码二维引力之外的黑洞内部增长方面具有特殊作用，同时凸显了算符和态概念下克雷洛夫复杂度之间的定性区别。
英文摘要
We investigate the growth of the black hole interior in three-dimensional gravity from the boundary theory. For the two-sided BTZ black hole, we propose a boundary reconstruction of the time dependence of a codimension-one surface in terms of correlation functions of smeared operators in the thermofield double state, reproducing the characteristic late-time linear growth predicted by the complexity-volume proposal. Using the Chern--Simons formulation of three-dimensional gravity, these nonlocal correlators are represented by bulk Wilson lines with smeared endpoints, extending the familiar connection between Wilson lines and codimension-two observables underlying holographic entanglement entropy to codimension-one observables. We then ask whether the same geometric growth is captured by Krylov complexity. For the smeared operators, we extract the Lanczos data from their correlation functions and find that operator Krylov complexity reproduces the late-time linear growth of the black hole interior, extending previous connections between operator growth and bulk geometry to AdS$_3$. By contrast, the Krylov spread complexity of the thermofield double state, obtained from the semiclassical gravitational partition function, does not exhibit the linear growth of the bulk volume within the regime accessible to our analysis. Our results therefore point to a distinguished role for operator Krylov complexity in encoding black hole interior growth beyond two-dimensional gravity, while highlighting a qualitative distinction between operator and state notions of Krylov complexity.
