Holographic thermal entropy and modular conjugation from geodesic bit threads

In this talk, I will discuss some new interesting properties of geodesic bit threads in static backgrounds.
Bit threads are an insightful tool for investigating holographic entanglement entropy, providing a reformulation of the Ryu-Takayanagi formula in terms of the maximal flux of a bounded and divergenceless vector field.
An explicit realization of bit threads is given by geodesic bit threads.
I will first argue that, for a spherical region on AdS boundary and for an interval on the BTZ boundary, geodesic bit threads display a surprising connection with modular conjugation in CFT.
Then, I will show that for an interval on the BTZ boundary and for a spherical region on the boundary of Schwarzschild AdS, the flux of geodesic bit threads hitting the event horizon provides the holographic thermal entropy, i.e. the product of a thermal entropy density with the volume of the spherical region.