Modular conjugations in 2D conformal field theory and holographic bit threads

TL;DR

This paper explores the geometric actions of modular conjugations in 2D conformal field theories and their holographic duals, revealing connections to geodesic bit threads and black hole horizons.

Contribution

It demonstrates how modular conjugations correspond to geodesic bit threads in the holographic dual, linking boundary modular maps to bulk geometric structures.

Findings

Modular conjugations correspond to geodesic bit threads in AdS/CFT.

Inversion maps relate to horizons in the BTZ black brane.

Constructed inversion map for massless Dirac fermion bipartitions.

Abstract

We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by an interval when the system is in the ground state, either on the line or on the circle, and in the thermal Gibbs state on the line. We find that the restriction of the corresponding inversion maps to a spatial slice is obtained also in the gauge/gravity correspondence through the geodesic bit threads in a constant time slice of the dual static asymptotically AdS background. For a CFT in the thermal state on the line, the modular conjugation suggests the occurrence of a second world which can be related through the geodesic bit threads to the horizon of the BTZ black brane background. An inversion map is constructed also for the massless Dirac fermion in the ground state and on the line bipartite by the union of two disjoint intervals.