A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and \(SL(2,\mathbb R)\) Lowest-Weight Structure

[2607.03800] A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and $SL(2,\mathbb R)$ Lowest-Weight Structure Skip to main content Search Submit Donate Log in High Energy Physics - Theory arXiv:2607.03800 (hep-th) [Submitted on 4 Jul 2026 ( v1 ), last revised 12 Oct 2026 (this version, v5)] Title: A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and $SL(2,\mathbb R)$ Lowest-Weight Structure Authors: Yoon-Seok Choun , Ki-Seok Kim View PDF HTML (experimental) Abstract: 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 $\chi_\mu$ denote the universal ingoing horizon factor. We find \[ \widehat A=0 \Longleftrightarrow \frac{R_2}{\chi_\mu}\in C^\infty, \qquad \widehat B=0 \Longleftrightarrow \frac{R_1}{\chi_\mu}\in C^\infty . \] 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. Subjects: High Energy Physics - Theory (hep-th) Cite as: arXiv:2607.03800 [hep-th] (or arXiv:2607.03800v5 [hep-th] for this version) https://doi.org/10.48550/arXiv.2607.03800 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ki Seok Kim [ view email ] [v1] Sat, 4 Jul 2026 10:08:47 UTC (273 KB) [v2] Sat, 18 Jul 2026 23:32:17 UTC (268 KB) [v3] Mon, 27 Jul 2026 15:01:18 UTC (268 KB) [v4] Tue, 25 Aug 2026 06:31:37 UTC (268 KB) [v5] Mon, 12 Oct 2026 23:35:24 UTC (435 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-07 References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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