A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and SL(2,ℝ) Lowest-Weight Structure
Abstract
We study pole-skipping for a scalar field in the JT/AdS2 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 R1 and R2 for the source and response branches, respectively. Let  and B̂ denote the source and response coefficients after their common singular factor is removed, and let χμ denote the universal ingoing horizon factor. We find Â=0 Longleftrightarrow R2/χμ∈ C∞, B̂=0 Longleftrightarrow R1/χμ∈ C∞ . 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 aN. In the JT/AdS2 model, continuation of the nonresonant ingoing solution fixes aN=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,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[R1,R2]≠0. These results distinguish the known local horizon degeneracy from the global relation between boundary branches and the resonant horizon solution space.
Related
- Fuchsian Resonance and a Horizon-to-Boundary Dictionary for Pole-Skipping
- Horizon-Boundary Localization of the Hawking Temperature in a Weak AdS/CFT Extension
- Horizon Structure and Geodesic Properties of Simpson-Visser Black Holes in Einstein-Euler-Heisenberg Theory
- Universal Structure of Horizon Formation in Generic Binary Black Hole Mergers
- Black holes from a nonlocal equation of state: horizon geometry, singularity structure and thermodynamics
BibTeX
@misc{choun2026horizontoboundary,
title = {{A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and $SL(2,\mathbb R)$ Lowest-Weight Structure}},
author = {Yoon-Seok Choun and Ki-Seok Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.03800},
eprint = {2607.03800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03800},
}
RIS
TY - UNPB
TI - A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and SL(2,ℝ) Lowest-Weight Structure
AU - Yoon-Seok Choun
AU - Ki-Seok Kim
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2607.03800
UR - https://arxiv.org/abs/2607.03800
AB - 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  and B̂ 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 Â=0 Longleftrightarrow R_2/χ_μ∈ C^∞, B̂=0 Longleftrightarrow R_1/χ_μ∈ C^∞ . 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,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]≠0. These results distinguish the known local horizon degeneracy from the global relation between boundary branches and the resonant horizon solution space.
ER -