黑洞视界分支选择的光滑性原理
A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and \(SL(2,\mathbb R)\) Lowest-Weight Structure
AI总结：
针对黑洞波方程在视界处的分支选择问题，提出移除主导视界行为并使剩余场 \(C^{\infty }\) 光滑的原理，用 \(JT/AdS_{2}\) 标量场证明该原理统一多种结构，还用于超导模型。
AI中文摘要：
许多黑洞波动方程在视界处简化为具有正则奇点的径向常微分方程，局部解分裂为不同分支。我们提出一个简单的分支选择原则来分离出物理上有区别的分支：去除主导的视界行为并对剩余场施加 \(C^{\infty }\) 光滑性。利用 \(JT/AdS_{2}\) 中一个可精确求解的标量场，我们证明这个单一原则成功地组织了三种看似不同的结构：跨越黑洞视界的光滑延续、边界延迟格林函数的模糊性（极点跳跃）以及 \(SL(2,\mathbb{R})\) 表示的最低权重结构。我们的结果不是将这些现象视为孤立的边界或视界属性，而是将它们统一成一个连贯的体到边界字典，证明边界极点跳跃模糊性是视界剩余光滑性的精确全息表现。此外，群论识别表明这种物理分支选择不仅仅是一个数学产物，而是从根本上由底层时空对称性控制。最后，我们将这个框架作为诊断工具应用于一个静态全息超导体模型，揭示一个真正的极点跳跃点需要同时具备剩余光滑性和边界分支的严格线性独立性，以防止欺骗性的分支坍缩伪像。
英文摘要：
We study pole-skipping for a scalar field in the JT/AdS$_2$ black-hole background. Previous work established the local mechanism: at a pole-skipping point, a near-horizon recurrence relation becomes degenerate and an additional regular expansion coefficient is left undetermined. We take this local degeneracy as the starting point and track two independent solutions normalized at the AdS boundary, denoted by $R_1$ and $R_2$ for the source and response branches, respectively. Let $\widehat A$ and $\widehat B$ denote the source and response coefficients after their common singular factor is removed, and let $χ_μ$ denote the universal ingoing horizon factor. We find \[ \widehat A=0 \Longleftrightarrow \frac{R_2}{χ_μ}\in C^\infty, \qquad \widehat B=0 \Longleftrightarrow \frac{R_1}{χ_μ}\in C^\infty . \] Thus the source and response zeros correspond separately to horizon smoothness of the two boundary-normalized solutions after the ingoing factor is removed. At integer resonance the local regular solution contains an additional coefficient $a_N$. In the JT/AdS$_2$ model, continuation of the nonresonant ingoing solution fixes $a_N=0$ and thereby selects a unique retarded value at resonance, although unrestricted approaches in parameter space remain path dependent. At the endpoint of the pole-skipping lattice, the response branch is a lowest-weight state of the background $SL(2,\mathbb R)$ symmetry. A static holographic-superconductor example further shows that simultaneous horizon smoothness is insufficient if the two boundary branches are linearly dependent. A two-branch pole-zero intersection therefore requires \[ W[R_1,R_2]\neq0. \] These results distinguish the known local horizon degeneracy from the global relation between boundary branches and the resonant horizon solution space.
