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

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 conformal field theory 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.

Holographic entanglement as nonlocal magnetism

“…Recent work by Freedman and Headrick demonstrated that the RT formula is amenable to a dual description in terms of flows, divergenceless norm-bounded vector fields, or alternatively, a collection of Planck-thickness "bit threads" [58]. This novel prescription has revealed hitherto undiscovered properties of holographic entanglement and has given them a neat information-theoretic interpretation in terms of distillation of EPR-type entanglement [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77]. Like the RT formula, bit threads have been extended to covariant settings [78], non-Einstein gravity theories [79], and when bulk quantum corrections are considered [80,81].…”

“…A handful of methods for computing particular thread configurations were introduced in [63,70]. Among these, the so-called "geodesic bit threads" were recently interpreted in terms of modular conjugations in the dual conformal field theory [75]. In the following, we will consider simple examples of such bit thread configurations.…”