Bit threads, Einstein’s equations and bulk locality

Agón, César A.; Cáceres, Elena; Pedraza, Juan F.

doi:10.1007/jhep01(2021)193

Cited by 32 publications

(91 citation statements)

References 76 publications

(202 reference statements)

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“…This is recently explored in [36] by applying the locking theorems [58,59] of bit threads to construct a concrete locking scheme for the RT surfaces in the entanglement wedge. In [60] two perturbations of the bit threads configurations are explicitly considered. One of them is for the geodesic bit threads normal to the RT surface [57], consistent with our fine structure analysis [29] 9 .…”

Section: Discussionmentioning

confidence: 99%

First law and quantum correction for holographic entanglement contour

Han

Wen²

2021

SciPost Phys.

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Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region AA to the first order perturbation of the expectation value of the modular Hamiltonian, \delta S_{A}=\delta \langle K_A \rangleδSA=δ⟨KA⟩. We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. \delta s_{A}(\textbf{x})=\delta \langle k_{A}(\textbf{x})\rangleδsA(𝐱)=δ⟨kA(𝐱)⟩. Here the contour functions s_{A}(\textbf{x})sA(𝐱) and k_{A}(\textbf{x})kA(𝐱) capture the contribution from the degrees of freedom at \textbf{x}𝐱 to S_{A}SA and K_AKA respectively. In some simple cases k_{A}(\textbf{x})kA(𝐱) is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the applies.

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Section: Discussionmentioning

confidence: 99%

First law and quantum correction for holographic entanglement contour

Han

Wen²

2021

SciPost Phys.

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“…In [37] the authors put forward an alternative formulation of the holographic entanglement entropy that does not rely on minimizing an area functional but invokes a divergenceless vector field, dubbed bit threads. Many aspects of bit threads have been studied [38][39][40][41][42][43], but a formulation of bit threads for higher-derivative theories was missing. Recently this gap was closed in [44], where the authors derived a bit thread formulation for a general higher-derivative theory.…”

Section: Bit Threadsmentioning

confidence: 99%

Entanglement entropy in cubic gravitational theories

Cáceres

Vásquez

López

2021

J. High Energ. Phys.

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We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

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“…Given the connection between JHEP05(2021)149 bit threads and entanglement distillation [115] (see also [162]), this could shed light on the interpretation of the new functional, even in the absence of a concrete boundary dual definition. Finally, one could also ask questions about bulk reconstruction and the emergence of spacetime (either using the generalized entropy S or the C-function) which have already provided tremendous insights in the program of gravitation from entanglement in holography [163][164][165][166][167][168][169].…”

Section: Jhep05(2021)149mentioning

confidence: 99%

Quantum information probes of charge fractionalization in large-N gauge theories

DiNunno

Jokela

Pedraza

et al. 2021

J. High Energ. Phys.

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We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

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Bit threads, Einstein’s equations and bulk locality

Cited by 32 publications

References 76 publications

First law and quantum correction for holographic entanglement contour

First law and quantum correction for holographic entanglement contour

Entanglement entropy in cubic gravitational theories

Quantum information probes of charge fractionalization in large-N gauge theories

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