AI 中文总结
该研究探究全息RG流中的Krylov扩展复杂度，推导其加速度与协变中心电荷的关系，发现跨维度流中二者呈共单调，为连接信息扩展、全息中心函数与RG演化提供了几何诊断工具。
AI 中文摘要
我们利用如下提议研究全息重整化群（RG）流中的Krylov扩展复杂度：其增长速率由下落的大质量探针的适当径向动量所捕获。我们聚焦于复杂度的二阶时间导数$U$，该量由对偶几何的红移和径向度规函数局域决定。对于保持时空维度的洛伦兹不变畴壁流，我们推导了$U$与协变中心电荷$c_{\text{cov}}$之间的新关系。协变中心函数向红外的减小伴随着复杂度加速度的单调增加。对于自顶向下的Dp-膜族，我们得到了一个普适关系。随后我们研究跨维度流，包括从四维到二维以及从六维到四维的扭曲紧致化。在这些例子中，$c_{\rm cov}$与$U$呈共单调关系，这与固定维度流所特有的逆相关性形成鲜明对比。我们认为这种反转反映了自由度在紧致化下向低维区域的重组，而非简单耗尽。我们的结果将复杂度加速度确定为一种敏感的几何诊断工具，可连接信息扩展、全息中心函数与RG演化。
英文摘要
We investigate Krylov spread complexity along holographic renormalisation-group flows using the proposal that its growth rate is captured by the proper radial momentum of an in-falling massive probe. We focus on the second time derivative of the complexity ${U}$, which is determined locally by the redshift and radial metric functions of the dual geometry. For Lorentz-invariant domain-wall flows preserving the spacetime dimension, we derive a new relation between ${U}$ and the covariant central charge $c_{\text{cov}}$. The decrease of the covariant central function towards the infrared is accompanied by a monotonic increase of the complexity acceleration. For the top-down Dp-brane family, we obtain a universal relation. We then examine flows across dimensions, including a twisted compactification from four to two dimensions and from six to four dimensions. In these examples $c_{\rm cov}$ and ${U }$ are co-monotonic, in sharp contrast with the inverse correlation characteristic of fixed-dimensional flows. We argue that this reversal reflects the reorganisation, rather than simple depletion, of degrees of freedom into lower-dimensional sectors under compactification. Our results identify complexity acceleration as a sensitive geometric diagnostic connecting information spreading, holographic central functions and RG evolution.
Comments20 pages, various figures
