The thread embodiment of holographic quantum entanglement

Abstract: In this paper, we systematically develop a holographic entanglement thread picture that characterizes the entanglement structure of holographic duality. Behind this construction lies a simple philosophy: holographic quantum entanglement can be visualized by thread-like objects. Inspired by tensor network models and the earlier concept of bit threads, we propose rules governing the trajectories of entanglement threads in the holographic bulk. These rules not only carry meaningful interpretations at the level of quantum information theory but also determine that the entanglement threads travel along geodesics in the holographic bulk. This makes kinematic space a tailor-made language for describing holographic entanglement thread configurations. We hope that the holographic entanglement thread method can provide necessary constraints or useful guidance for constructing genuine holographic tensor networks beyond toy models.