Gravity Dual of Connes Cocycle Flow

TL;DR

This paper introduces the kink transform as a bulk dual to Connes cocycle flow, linking boundary CC flow to a specific bulk geometry with shock features, advancing holographic understanding of operator dynamics.

Contribution

It proposes the kink transform as a novel bulk dual to CC flow, providing a geometric construction that captures shock phenomena and extends previous holographic models.

Findings

Kink transform reproduces boundary CC flow effects holographically.

The bulk dual involves a Wheeler-DeWitt patch with shock features.

New shock components are derived from the kink transform.

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.