Theory Group Seminar, 25 September 2018

Cesar Alfonso Agón Quintero

Geometric Aspects of Holographic Bit Threads

abstract

In this talk I will review the recent reformulation of the Ryu-Takayanagi formula in terms of a convex optimization problem introduced by Freedman and Headrick. According to them, the holographic entanglement entropy associated to a boundary region is given by the maximum flux of a bounded, divergence-less bulk vector field through the corresponding region. I will present a general algorithm that allows the construction of explicit instantiations of such vector fields (or bit-threads) in cases in which the minimal surface is known, and will illustrate the method with simple examples such as a sphere and a strip in vacuum AdS, and a strip in a BTZ black hole. We also consider the case of disjoint regions on which one can explicitly construct the so called multi-commodity flows and with that illustrate the monogamy property of mutual information which was only recently proved in the language of bit threads. We also study bit-thread configurations which simultaneously compute the entanglement entropy and the entanglement of purification of a given boundary region and comment on their interpretation.