Abstract
We define the "kink transform" as a one-sided boost of bulk initial data about the Ryu-Takayanagi surface of a boundary cut. For a flat cut, we conjecture that the resulting Wheeler-DeWitt patch is the bulk dual to the boundary state obtained by Connes cocycle (CC) flow across the cut. The bulk patch is glued to a precursor slice related to the original boundary slice by a one-sided boost. This evades ultraviolet divergences and distinguishes our construction from one-sided modular flow. We verify that the kink transform is consistent with known properties of operator expectation values and subregion entropies under CC flow. CC flow generates a stress tensor shock at the cut, controlled by a shape derivative of the entropy; the kink transform reproduces this shock holographically by creating a bulk Weyl tensor shock. We also go beyond known properties of CC flow by deriving novel shock components from the kink transform.
Highlights
The anti–de Sitter (AdS)=CFT duality [1,2,3] has led to tremendous progress in the study of quantum gravity
The study of modular operators led to the result that the boundary relative entropy in a region A equals the bulk relative entropy in its entanglement wedge EWðAÞ [7]
We prove that the new initial data satisfy the gravitational constraint equations, demonstrating that the kink transform defines a valid bulk spacetime Ms We show that Ms is independent of the choice of Σ
Summary
The AdS=CFT duality [1,2,3] has led to tremendous progress in the study of quantum gravity. The study of modular operators led to the result that the boundary relative entropy in a region A equals the bulk relative entropy in its entanglement wedge EWðAÞ [7]. The kink transform separately preserves the entanglement wedges of A and A0, but it glues them together with a relative boost by rapidity 2πs This implies the one-sided expectation values and subregion entropies of the CC flowed state ψs are correctly reproduced when they are computed holographically in the bulk spacetime Ms We perform a more nontrivial check of this proposal. Our proposal follows from an extended version of the JLMS result, which includes nonperturbatively different background geometries Equipped with this understanding, we can distinguish our proposal from the closely related bulk duals of one-sided modular flowed states [25,26]. In the Appendix, we derive the null limit of the kink transform and show that it generates a Weyl shock, which provides intuition for how the kink transform modifies gravitational observables
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