Bit Threads: From Entanglement to Geometric Entropies

TL;DR

This paper develops a method to construct bit thread configurations in holographic spacetimes, relating entanglement entropy to geometric and quantum effects, and explores their applications in various backgrounds.

Contribution

It introduces a covariant phase space approach to construct bit threads, connecting them with Wald and differential entropy, and extends the framework to dynamical spacetimes with quantum effects.

Findings

Bit thread configurations are constructed for different backgrounds.

The relation between bit threads, Wald entropy, and differential entropy is clarified.

Quantum effects impose constraints on bulk entanglement via energy conditions.

Abstract

In this work, we attempt to construct bit thread configurations for various backgrounds using expressions from the covariant phase space formalism. We find that when the Ryu-Takayanagi surface is same as the horizon, such expressions are sufficient. In other cases, it differs by gradient of a harmonic function. We explore its relation to Wald and differential entropy, and re-express the first law of entanglement entropy in terms of bit threads. Inclusion of quantum effects imposes some constraints on the bulk entanglement via the dominant energy condition. We also apply our method to ascertain a bit thread configuration in a certain dynamical spacetime.