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<p>We model the Hayden-Preskill (HP) information recovery protocol in 2d CFTs via local joining quenches. Euclidean path integrals with slits prepare the HP subsystems: the message <i>M</i>, its reference <i>N</i>, the Page-time black hole <i>B</i>, the early radiation <i>E</i>, and the late radiation <i>R</i>; the remaining black hole after emitting <i>R</i> is denoted as <i>B</i><sup>′</sup>. The single-slit geometry provides an analytically tractable toy model, while the bounded-slit geometry more closely captures the HP setup. In the free Dirac fermion 2d CFT, the mutual information <i>I</i>(<i>N</i> : <i>B</i><sup>′</sup>) shows quasi-particle dynamics with partial or full revivals, whereas that in holographic 2d CFTs, which are expected to be maximally chaotic, exhibits sharp transitions: in the bounded-slit case, when the size of the late radiation becomes comparable to that of the reference <i>N</i>, <i>I</i>(<i>N</i> : <i>B</i><sup>′</sup>) vanishes at late time, otherwise it remains finite. This contrast between free CFTs and holographic CFTs gives a clear characterization of the HP recovery threshold.</p>

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Hayden-Preskill model via local quenches

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  • 发表日期：

    2026年3月24日

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  • Weibo Mao,
  • Tadashi Takayanagi

摘要

We model the Hayden-Preskill (HP) information recovery protocol in 2d CFTs via local joining quenches. Euclidean path integrals with slits prepare the HP subsystems: the message M, its reference N, the Page-time black hole B, the early radiation E, and the late radiation R; the remaining black hole after emitting R is denoted as B′. The single-slit geometry provides an analytically tractable toy model, while the bounded-slit geometry more closely captures the HP setup. In the free Dirac fermion 2d CFT, the mutual information I(N : B′) shows quasi-particle dynamics with partial or full revivals, whereas that in holographic 2d CFTs, which are expected to be maximally chaotic, exhibits sharp transitions: in the bounded-slit case, when the size of the late radiation becomes comparable to that of the reference N, I(N : B′) vanishes at late time, otherwise it remains finite. This contrast between free CFTs and holographic CFTs gives a clear characterization of the HP recovery threshold.