AI 中文总结
研究近极端全息黑洞中高阶极点跳跃，开发系统分析方法，通过重新组织近视界弗罗贝尼乌斯展开揭示温度分级结构，将极点跳跃条件简化为代数方程，计算主导温度修正并经数值分析验证，为极点跳跃点提供解析途径并阐明全息格林函数结构。
AI 中文摘要
我们开发了一种系统的分析方法来研究近极端全息黑洞中的高阶极点跳跃。在近极端区域，接近\(T\to0\)极限时，近视界几何发展出近似\(\mathrm{AdS}_2\times\mathbb{R}^{d - 1}\)结构。我们表明，标记极点跳跃点的模式指标\(q\)与出现的\(\mathrm{AdS}_2/\mathrm{CFT}_1\)对应中的红外共形维度\(\Delta_{\mathrm{IR}} = q\)一致，为次主导极点跳跃塔提供了具体的物理解释。该方法根据温度幂次重新组织近视界弗罗贝尼乌斯展开，揭示了温度分级的层次结构，将\(n\)阶极点跳跃条件简化为因式分解的代数方程，每个极点跳跃动量仅取决于模式指标\(q\)，而非阶数\(n\)。当\(T\to0\)时，这种\(n\)独立性产生高度简并，所有阶的极点跳跃动量坍缩到由近视界几何和标量场质量确定的离散值集上，这些值可用熵密度和比热等热力学量表示。在\(n\gg1\)（\(nT\)保持小）的极限下，主导极点跳跃动量渐近增长为\(k_{n,n}\propto n\)。我们计算主导温度修正，并通过对双荷古布泽 - 罗查模型的数值分析验证我们的预测。结果证实低温下的高阶极点跳跃由近视界物理控制，这为远超标准行列式方法可及的极点跳跃点提供了解析途径，并阐明了低温区域全息格林函数的结构。
英文摘要
We develop a systematic analytic method for studying high-order pole-skipping in near-extremal holographic black holes. In the near-extremal regime, approaching the limit $T\to0$, the near-horizon geometry develops an approximately $\mathrm{AdS}_2 \times \mathbb{R}^{d-1}$ structure; we show that the mode index $q$ labeling pole-skipping points is identified with the IR conformal dimension $Δ_{\mathrm{IR}} = q$ in the emergent $\mathrm{AdS}_2/\mathrm{CFT}_1$ correspondence, providing a concrete physical interpretation of the subleading pole-skipping tower. The method reorganizes the near-horizon Frobenius expansion according to powers of temperature. This reveals a temperature-graded hierarchical structure that reduces the $n$-th-order pole-skipping condition to a factorized algebraic equation:each pole-skipping momentum depends only on the mode index $q$, not on the order $n$. This $n$-independence produces a high degeneracy as $T\to 0$, where pole-skipping momenta at all orders collapse onto a discrete set of values determined by near-horizon geometry and the scalar field mass; these values can be expressed in terms of thermodynamic quantities such as entropy density and specific heat. In the limit $n \gg 1$ (with $nT$ remaining small), the leading pole-skipping momenta grow asymptotically as $k_{n,n} \propto n$. We compute leading temperature corrections and verify our predictions through numerical analysis of the Dyonic Gubser--Rocha model. The results confirm that high-order pole-skipping at low temperature is governed by near-horizon physics. This provides analytic access to pole-skipping points well beyond those accessible by standard determinant methods and clarifies the structure of holographic Green's functions in the low-temperature regime.
Comments17 pages, many figures,2 tables, Phys. Rev.D in press
