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<p>The connected wedge theorem [1, 2] states that in order to have a scattering process in the bulk, it is necessary to have <i>O</i>(1/<i>G</i><sub><i>N</i></sub>) mutual information between certain “decision” regions in the boundary theory. While this large mutual information is not generally sufficient to imply scattering, [3] showed that for a certain class of geometries, bulk scattering is implied by a certain relation between two (possibly non-minimal) Ryu-Takayanagi surfaces. Here, we show that the 2-to-2 version of the theorem becomes an equivalence in pure AdS<sub>3</sub>: large mutual information between appropriate boundary subregions is both necessary and sufficient for bulk scattering. This result allows us to extend the findings of [3] to a broader class of asymptotically AdS<sub>3</sub> spacetimes, which we illustrate with the spinning conical defect geometry. In contrast, we find that matter sources can disrupt this converse relation, and that the <i>n</i>-to-<i>n</i> version of the theorem with <i>n</i> &gt; 2 lacks a converse even in the AdS<sub>3</sub> vacuum.</p>

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The geodesics less traveled: Nonminimal RT surfaces and holographic scattering

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月20日

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  • Jacqueline Caminiti,
  • Caroline Lima,
  • Robert C. Myers

摘要

The connected wedge theorem [1, 2] states that in order to have a scattering process in the bulk, it is necessary to have O(1/GN) mutual information between certain “decision” regions in the boundary theory. While this large mutual information is not generally sufficient to imply scattering, [3] showed that for a certain class of geometries, bulk scattering is implied by a certain relation between two (possibly non-minimal) Ryu-Takayanagi surfaces. Here, we show that the 2-to-2 version of the theorem becomes an equivalence in pure AdS3: large mutual information between appropriate boundary subregions is both necessary and sufficient for bulk scattering. This result allows us to extend the findings of [3] to a broader class of asymptotically AdS3 spacetimes, which we illustrate with the spinning conical defect geometry. In contrast, we find that matter sources can disrupt this converse relation, and that the n-to-n version of the theorem with n > 2 lacks a converse even in the AdS3 vacuum.