Holographic Entanglement Entropy using Bit Threads

Abstract

It is known that the entanglement entropy of a region in a CFT can be holographically mapped to the Ryu-Takayanagi(RT) surface. This is the minimal surface in AdS homologous to the entangling region. In this project, we use the bit thread interpretation of the RT formula. We investigate if it can be used to find a more concrete algorithm for calculating the entanglement entropy of a given entangling region. Our first results are promising, recovering the right bit thread configurations for specific cases in time slices of two and three-dimensional CFT's. However, a careful analysis reveals that a generalization to arbitrary entangling regions should be shape-dependent. For the case of a three-dimensional CFT, the bit thread prescription suggests a generalized Biot-Savart law that depends on the local curvature of the entangling surface.