Bulk locality from modular flow

Recent works have suggested that the entanglement wedge of Hawking radiation coming from an AdS black hole, will include an island inside the black hole interior after the Page time. In this paper, we propose a concrete way to extract the information from the island by acting only on the radiation degrees of freedom, building on the equivalence between the boundary and bulk modular flow. We consider examples with black holes in JT gravity coupled to baths. In the case that the bulk conformal fields contain free massless fermion field, we provide explicit bulk picture of the information extraction process, where we find that one can almost pull out an operator from the island to the bath with modular flow.

Section: Pulling Out the Islandmentioning

confidence: 99%

Pulling out the island with modular flow

Chen

2020

“…There is a large literature on bulk reconstruction in AdS/CFT employing a variety of philosophies and methods, for example [1,2,4,[12][13][14][15][17][18][19][20][21][22][23][24][25][26][27][28]. 1 The most common approach expresses bulk fields in terms of local CFT operators integrated against a kernel [1,2,18].…”

Section: Jhep02(2018)012mentioning

confidence: 99%

“…From the bulk or WheelerDeWitt perspective, the formation and evaporation of a black hole can be pure gauge! Many recent works have focused on the relationship between bulk and boundary domains of dependence [25,[38][39][40][41] in Lorentzian signature. Some of this work [42] was motivated by putative ambiguities in bulk reconstruction associated with the fact that a bulk operator φ(X) can be expressed using smearing functions supported on different boundary domains [2].…”

Section: Jhep02(2018)012mentioning

confidence: 99%

An exact operator that knows its location

Anand

Chen

Fitzpatrick

et al. 2018

121

We use conformal symmetry to define an AdS 3 proto-field φ as an exact linear combination of Virasoro descendants of a CFT 2 primary operator O. We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator φ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large c, and that automatically take the correct form in all vacuum AdS 3 geometries, including BTZ black hole backgrounds. In the future it should be possible to use φ to probe bulk locality and black hole horizons at a non-perturbative level.

“…As a result, the entanglement wedges (for a quick definition see 3.1) are empty. This means that the density matrices of these subsystems are proportional to identity because for each of these subsystems the density matrix commutes with all local operators inside it (see [23] for more of this point of view and the entanglement wedge). Hence the states of subsystems with size smaller than half of the whole are maximally mixed (this is confirmed in [5] for DS 3 from an explicit field theory calculation).…”

Section: Energy Spectrum For Pure Dsmentioning

confidence: 99%

Some information theoretic aspects of de-Sitter holography

Geng¹

2020

Built on our observation that entangling surfaces of the boundary field theory are great co-dimension one spheres in the context of DS/dS correspondence, we study some information theoretic quantities of the field theory dual intensively using holographic proposals. We will focus on entanglement entropy (EE), entanglement of purification (EoP) and complexity. Several fundamental observations and analysis are provided. For EE, we focus on its scaling behavior, which indicates the nature of the relevant degrees of freedom. Moreover, we find that EE provides us with important information of the energy spectrum in pure dS and it also leads us to the speculation that the field theory dual is chaotic or non-integrable. For EoP, an interesting phenomenon we call "Entanglement Wedge Cross Section (EWCS) Jump" is observed according to which we propose two puzzles regarding EoP and EE in the context of dS holography. For complexity, we find that the Complexity=Volume proposal does not provide a well-defined way to compute complexity for pure dS. However, it does provide a well-defined way to compute complexity in the TT + Λ 2 deformed case. At the end, we will use the surface/state correspondence to resolve all the puzzles and hence reach a consistent information theoretic picture of dS holography. Moreover, we will provide evidence for our former proposal that the TT + · · · deformations are operating quantum circuits and study the non-locality of the field theory algebra suggested by the surface/state correspondence. arXiv:1911.02644v3 [hep-th] 30 Dec 2019 1 I thank Eva Silverstein for pointing out that some very recent developments addressing these questions are made in [5] and references therein.