Hayden-Preskill model via local quenches

A bstract 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.