Flat entanglement spectra in fixed-area states of quantum gravity

Dong, Xi; Harlow, Daniel; Marolf, Donald

doi:10.48550/arxiv.1811.05382

Cited by 32 publications

(79 citation statements)

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“…The role of the cosmic brane is like a sharp projection that maps the original geoemtry M ψ to the fixed area geometry. The above results are consistent with the discussion in [11] by using the gravitational path integral. As a check of the above statement, let's consider the vacuum state in AdS 3 .…”

Section: Pure Geometric States As Superposition Of Fixed Area Statessupporting

confidence: 92%

“…One of the interesting result is the pure geometric state |ψ can be approximated by the state ρ ψ t with t = S(ρ ψ A ) − S ∞ (ρ ψ A ) for the holographic CFTs [10]. Moreover, this state has flat spetra, thus the Rényi entropy is independent with n. The so-called fixed area states constructed in [11] also show the same property. Their approach is based on the graviational path integral with inserting a cosmic brane fixed to be on the RT surface.…”

Section: Introductionmentioning

confidence: 85%

“…For the holographic CFT b ∼ O(c) ≫ 1, taking t to be the order of c. The density of state c). By construction the Rényi entropy of the state ρ t,A is same as the EE, which is an important feature for the so-called fixed area states [11]. In the following we would like to show the state |Φ t is a fixed area state by explicitly constructing the bulk geometry.…”

Section: Vacuum State: An Explicit Examplementioning

confidence: 99%

“…However, the contributions from t ≪ c are usually exponentially suppressed in the large c limit. We can safely take the vacuum state of a holographic CFT as superposition of fixed area states by introducing a lower cut-off of the integral (11).…”

Section: Pure Geometric States As Superposition Of Fixed Area Statesmentioning

confidence: 99%

“…Moreover, M n can be constructed by cyclically gluing n-copy geometry (6) together along the defect line γ. In [11] the fixed area states are constructed in the way as we have stated above. The conical defect line can be realized by inserting codimension-2 cosmic branes (lines in AdS 3 ).…”

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confidence: 99%

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The area operator and fixed area states in conformal field theories

Guo¹

2021

Preprint

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The fixed area states are constructed by gravitational path integrals in previous studies. In this paper we show the dual of the fixed area states in conformal field theories (CFTs). These CFT states are constructed by using spectrum decomposition of reduced density matrix ρA for a subsystem A.For 2 dimensional CFTs we directly construct the bulk metric, which is consistent with the expected geometry of the fixed area states. For arbitrary pure geometric state |ψ in any dimension we also find the consistency by using the gravity dual of Rényi entropy. We also give the relation of parameters for the bulk and boundary state. The pure geometric state |ψ can be expanded as superposition of the fixed area states. Motivated by this, we propose an area operator Âψ . The fixed area state is the eigenstate of Âψ , the associated eigenvalue is related to Rényi entropy of subsystem A in this state. The Ryu-Takayanagi formula can be expressed as the expectation value ψ| Âψ |ψ divided by 4G, where G is the Newton constant. We also show the fluctuation of the area operator in the geometric state |ψ is suppressed in the semiclassical limit G → 0.

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Section: Pure Geometric States As Superposition Of Fixed Area Statessupporting

confidence: 92%

Section: Introductionmentioning

confidence: 85%

Section: Vacuum State: An Explicit Examplementioning

confidence: 99%

Section: Pure Geometric States As Superposition Of Fixed Area Statesmentioning

confidence: 99%

mentioning

confidence: 99%

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The area operator and fixed area states in conformal field theories

Guo¹

2021

Preprint

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Gravity edges modes and Hayward term

Takayanagi

Tamaoka

2020

J. High Energ. Phys.

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We argue that corner contributions in gravity action (Hayward term) capture the essence of gravity edge modes, which lead to gravitational area entropies, such as the black hole entropy and holographic entanglement entropy. We explain how the Hayward term and the corresponding edge modes in gravity are explained by holography from two different viewpoints. One is an extension of AdS/CFT to general spacetimes and the other is the AdS/BCFT formulation. In the final part, we explore how gravity edge modes and its entropy show up in string theory by considering open strings stuck to a Rindler horizon.

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Unambiguous phase spaces for subregions

Kirklin

2019

J. High Energ. Phys.

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The covariant phase space technique is a powerful formalism for understanding the Hamiltonian description of covariant field theories. However, applications of this technique to problems involving subregions, such as the exterior of a black hole, have heretofore been plagued by ambiguities arising at the boundary. We provide a resolution of these ambiguities by directly computing the symplectic structure from the path integral, showing that it may be written as a contour integral around a partial Cauchy surface. We comment on the implications for gauge symmetry and entanglement.

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Flat entanglement spectra in fixed-area states of quantum gravity

Cited by 32 publications

References 0 publications

The area operator and fixed area states in conformal field theories

The area operator and fixed area states in conformal field theories

Gravity edges modes and Hayward term

Unambiguous phase spaces for subregions

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