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<p>In the context of asymptotic 2-to-2 scattering process in AdS/CFT, the Connected Wedge Theorem identifies the existence of <i>O</i>(1<i>/G</i><sub><i>N</i></sub>) mutual information between suitable boundary subregions, referred to as decision regions, as a necessary but not sufficient condition for bulk-only scattering processes, i.e., nonempty bulk scattering region <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathcal{S}}_{0}\)</EquationSource> </InlineEquation>. Recently, Liu and Leutheusser proposed an enlarged bulk scattering region <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathcal{S}}_{E}\)</EquationSource> </InlineEquation> and conjectured that the non-emptiness of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathcal{S}}_{E}\)</EquationSource> </InlineEquation> fully characterizes the existence of <i>O</i>(1<i>/G</i><sub><i>N</i></sub>) mutual information between decision regions. Here, we provide a geometrical or general relativity proof for a slightly modified version of their conjecture.</p>

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A proof of the generalized Connected Wedge Theorem

  • 期刊论文

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  • 发表日期：

    2026年1月5日

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  • Bowen Zhao

摘要

In the context of asymptotic 2-to-2 scattering process in AdS/CFT, the Connected Wedge Theorem identifies the existence of O(1/GN) mutual information between suitable boundary subregions, referred to as decision regions, as a necessary but not sufficient condition for bulk-only scattering processes, i.e., nonempty bulk scattering region \({\mathcal{S}}_{0}\) . Recently, Liu and Leutheusser proposed an enlarged bulk scattering region \({\mathcal{S}}_{E}\) and conjectured that the non-emptiness of \({\mathcal{S}}_{E}\) fully characterizes the existence of O(1/GN) mutual information between decision regions. Here, we provide a geometrical or general relativity proof for a slightly modified version of their conjecture.