2026/07/04 by Yoon-Seok Choun, Ki-Seok Kim
#hep-th
Understanding how fields behave near black-hole horizons is central to solving the puzzle of quantum gravity and holographic dualities. While the ingoing boundary condition typically selects a unique retarded response, special resonant frequencies induce a mathematical ambiguity in which the response becomes indeterminate -- a phenomenon known as pole-skipping. Here we show that this ambiguity has a precise horizon origin and admits a unique causal resolution. By analytically tracking a scalar field in an exactly solvable two-dimensional black hole, we demonstrate that pole-skipping emerges precisely when two distinct boundary branches simultaneously achieve smooth, singularity-free continuations at the horizon. This structure is governed by an underlying spacetime conformal symmetry, while a branch-preserving continuation uniquely selects the causal response. Furthermore, we introduce a strict linear-independence criterion to distinguish genuine resonances from spurious branch-collapse points in holographic superconductors. Our work reveals that horizon regularity, causal continuation, and spacetime symmetry unify seemingly disparate bulk structures -- including Frobenius freedom, conformal representation towers, and the resolution of boundary ambiguities. This establishes a rigorous horizon-to-boundary dictionary that sharpens how local horizon physics and spacetime symmetries constrain nonlocal observables in holographic systems.