Lorentzian threads and generalized complexity

The holographic bit threads are an insightful tool to investigate the holographic entanglement entropy and other quantities related to the bipartite entanglement in AdS/CFT. We mainly explore the geodesic bit threads in various static backgrounds, for the bipartitions characterized by either a sphere or an infinite strip. In pure AdS and for the sphere, the geodesic bit threads provide a gravitational dual of the map implementing the geometric action of the modular conjugation in the dual CFT. In Schwarzschild AdS black brane and for the sphere, our numerical analysis shows that the flux of the geodesic bit threads through the horizon gives the holographic thermal entropy of the sphere. This feature is not observed when the subsystem is an infinite strip, whenever we can construct the corresponding bit threads. The bit threads are also determined by the global structure of the gravitational background; indeed, for instance, we show that the geodesic bit threads of an arc in the BTZ black hole cannot be constructed.

Holographic thermal entropy from geodesic bit threads

Caggioli,

Gentile,

Seminara

et al. 2024

Towards bit threads in general gravitational spacetimes

Du,

Sun

2024

The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region a possesses an associated generalized entanglement wedge E(a) ⊃ a on a static Cauchy surface M in general gravitational spacetimes, where E(a) may contain an entanglement island I(a). It suggests that the fine-grained entropy for bulk region a is given by the generalized entropy Sgen(E(a)). Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy Sgen(E(a)) of a bulk gravitational region a is established on the static Cauchy surface M, such that Sgen(E(a)) is equal to the maximum flux of any flow that starts from the boundary ∂M and ends at bulk region a, or equivalently, the maximum number of bit threads that connect the boundary ∂M to the bulk region a. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region E(a) \ a, particularly on an entanglement island region I(a) ⊂ (E(a) \ a), as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes.

Kasner eons with matter: holographic excursions to the black hole singularity

Cáceres,

Murcia,

Patra

et al. 2024

Recent work has shown that introducing higher-curvature terms to the Einstein-Hilbert action causes the approach to a space-like singularity to unfold as a sequence of Kasner eons. Each eon is dominated by emergent physics at an energy scale controlled by higher-curvature terms of a given order, transitioning to higher-order eons as the singularity is approached. The purpose of this paper is twofold. First, we demonstrate that the inclusion of matter dramatically modifies the physics of eons compared to the vacuum case. We illustrate this by considering a family of quasi-topological gravities of arbitrary order minimally coupled to a scalar field. Second, we investigate Kasner eons in the interior of black holes with field theory duals and analyze their imprints on holographic observables. We show that the behavior of the thermal a-function, two-point functions of heavy operators, and holographic complexity can capture distinct signatures of the eons, making them promising tools for diagnosing stringy effects near black hole singularities.