Homology Conditions for RT Surfaces in Double Holography

Dominik Neuenfeld

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Homology Conditions for RT Surfaces in Double Holography

Dominik Neuenfeld

High Energy Physics - Theory · Submitted 3 May 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We argue that the correct homology constraint for Ryu-Takayanagi surfaces depends on which of those $d$-dimensional perspectives is taken.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Recently, a novel formula for computing entropy in theories coupled to semi-classical gravity has been devised. Using this so-called island formula the entropy of semi-classical black holes follows a Page curve. Here, we study the relation between this novel entropy and semi-classical entropy in the context of doubly-holographic models. Double holography allows for two different $d$-dimensional descriptions of a black hole coupled to a non-gravitational bath, both of which allow a holographic computation of von Neumann entropy in bath subregions. We argue that the correct homology constraint for Ryu-Takayanagi surfaces depends on which of those $d$-dimensional perspectives is taken. As a consequence the von Neumann entropies of a fixed subregion in both descriptions can disagree. We discuss how the von Neumann entropies in both descriptions are related to the entropy computed by the island formula and coarse grained entropy. Moreover, we argue that the way operators transform between the two descriptions depends on their complexity. A simple toy model is introduced to demonstrate that a sufficiently complicated map between two descriptions of the system can give rise to an island formula and wormholes. Lastly, we speculate about the relation between double-holography and black hole complementarity.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recently, a novel formula for computing entropy in theories coupled to semi-classical gravity has been devised.	background 1.00	0.05	0.02	asserted 1.00
s1	Using this so-called island formula the entropy of semi-classical black holes follows a Page curve.	background 0.98	0.08	0.04	asserted 1.00
s2	Here, we study the relation between this novel entropy and semi-classical entropy in the context of doubly-holographic models.	contribution 0.98	0.76	0.05	asserted 0.90
s3	Double holography allows for two different $d$-dimensional descriptions of a black hole coupled to a non-gravitational bath, both of which allow a holographic computation of von Neumann entropy in bath subregions.	background 0.94	0.09	0.06	asserted 0.99
s4	We argue that the correct homology constraint for Ryu-Takayanagi surfaces depends on which of those $d$-dimensional perspectives is taken.	result 0.63	0.78	0.52	asserted 0.69
s5	As a consequence the von Neumann entropies of a fixed subregion in both descriptions can disagree.	result 0.84	0.66	0.26	asserted 0.94
s6	We discuss how the von Neumann entropies in both descriptions are related to the entropy computed by the island formula and coarse grained entropy.	contribution 0.87	0.81	0.12	asserted 0.71
s7	Moreover, we argue that the way operators transform between the two descriptions depends on their complexity.	result 0.52	0.74	0.08	asserted 0.76
s8	A simple toy model is introduced to demonstrate that a sufficiently complicated map between two descriptions of the system can give rise to an island formula and wormholes.	method 0.77	0.91	0.08	asserted 0.93
s9	Lastly, we speculate about the relation between double-holography and black hole complementarity.	future work 0.86	0.28	0.06	speculative 1.00

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from argument 0.96.

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arXiv listing abstract v3

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T body sentences
C citations
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The paper

Original abstract

Recently, a novel formula for computing entropy in theories coupled to semi-classical gravity has been devised. Using this so-called island formula the entropy of semi-classical black holes follows a Page curve. Here, we study the relation between this novel entropy and semi-classical entropy in the context of doubly-holographic models. Double holography allows for two different $d$-dimensional descriptions of a black hole coupled to a non-gravitational bath, both of which allow a holographic computation of von Neumann entropy in bath subregions. We argue that the correct homology constraint for Ryu-Takayanagi surfaces depends on which of those $d$-dimensional perspectives is taken. As a consequence the von Neumann entropies of a fixed subregion in both descriptions can disagree. We discuss how the von Neumann entropies in both descriptions are related to the entropy computed by the island formula and coarse grained entropy. Moreover, we argue that the way operators transform between the two descriptions depends on their complexity. A simple toy model is introduced to demonstrate that a sufficiently complicated map between two descriptions of the system can give rise to an island formula and wormholes. Lastly, we speculate about the relation between double-holography and black hole complementarity.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Reflected entropy and islands in JT gravity from partial dimensional reduction
hep-th 2026-10 conditional novelty 6.0 of 10

Reflected entropy computed in JT gravity from partial dimensional reduction reproduces the island/defect dictionary at first order in the brane fluctuation, with Page-like curves and Markov gaps that reorganize inside...
Monogamous quantum corrections to holographic mutual information
hep-th 2026-09 conditional novelty 6.0 of 10

An extensive bulk mutual-information model in AdS, realized by a free massive Dirac fermion, places the quantum-corrected boundary entropy vector inside the holographic entropy cone and reproduces fermionic generalize...
Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
hep-th 2021-12 conditional novelty 6.0 of 10

At finite temperature in a doubly holographic black string, entanglement islands exist below the critical brane angle but are confined to a finite region on the brane, giving a two-parameter phase structure of constan...
Holographic BCFTs and Communicating Black Holes
hep-th 2021-04 conditional novelty 6.0 of 10

The entanglement entropy of a strip BCFT with mismatched boundary conditions matches between a two-Karch-Randall-brane AdS3 dual and a twist-operator CFT calculation, and the dual implies a gap in the boundary conditi...
Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane
hep-th 2022-02 accept novelty 5.0 of 10

For a two-dimensional eternal black hole on a tensionful brane coupled to finite-size baths, the Page curve saturates either at the bath thermal entropy or at twice the brane black hole horizon entropy, depending on b...

Show 1 more citing papers

Page Curve from Defect Extremal Surface and Island in Higher Dimensions
hep-th 2021-05 conditional novelty 5.0 of 10

In 2+1 dimensions the defect extremal surface and island formula give identical Page curves, but in higher dimensions the defect extremal surface gives systematically smaller entropy, which the authors read as a UV co...

How the literature uses it

32 arXiv papers cite this in 45 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 21 sentences without a confident label

Uses its method or tool 1 paper

In this section, we closely follow Ref [ref] and rederive Hawking's result using the black hole radiation (name it $N$) along with its interior $I$ and understand the QIEM.

Redefining entanglement entropy -- can it solve the information paradox? · The Qubit Island Entropy Model(QIEM) · 0.83

Compares with it 1 paper

Note added: While we were writing this paper, we got aware of an interesting work [ref] , where subregion correspondence in double holography is independently considered in a setup similar to ours discussed in section [ref], but from a different perspective.

Causal Structures and Nonlocality in Double Holography · Introduction · 0.92

Cites it as background 20 papers

In these models [ref] (see also [ref] for related studies), the black hole is living on the KR brane and is coupled to a finite temperature bath modeled by a conformal field theory (CFT) on a manifold with a boundary.

Holographic BCFTs and Communicating Black Holes · Introduction · 0.91
Within this framework, a profound connection emerges among three entities: the bulk AdS spacetime denoted as $ℳ$, the holographic BCFT residing on $Σ$, and an intermediate picture where the braneworld $Q$ is coupled to a non-gravitating bath CFT located on the asymptotic boundary $Σ$ [ref] .[We assume $∂ℳ=Q∪Σ$, and the neglected edge term plays no role in this paper.] This triangle equivalence is often called double holography and has also played a key role in recent studies of evaporating black holes [ref] .

Exploring causality in braneworld/cutoff holography via holographic scattering · Introduction · 0.88
Refs. [ref] extensively studied quantum extremal islands and the Page curve in the context of doubly holographic models – see also [ref] .

Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane · Braneworld black holes · 0.99

What it cites · 129 sentences without a confident label

Builds on 3 papers

Extrapolating the results of [ref] to extremal surfaces which can be anchored on the boundary we thus have that for a bath subregion $A$ [equation] i.e., the brane perspective von Neumann entropy is a coarse grained entropy in the boundary perspective.

Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy · Mapping Entropies between the two Perspectives · 0.99
Extrapolating the results of [ref] to extremal surfaces which can be anchored on the boundary we thus have that for a bath subregion $A$ [equation] i.e., the brane perspective von Neumann entropy is a coarse grained entropy in the boundary perspective.

Coarse Graining Holographic Black Holes · Mapping Entropies between the two Perspectives · 0.99
Extrapolating the results of [ref] to extremal surfaces which can be anchored on the boundary we thus have that for a bath subregion $A$ [equation] i.e., the brane perspective von Neumann entropy is a coarse grained entropy in the boundary perspective.

A World without Pythons would be so Simple · Mapping Entropies between the two Perspectives · 0.99

Uses the method or tool of 1 paper

We can thus use HKLL for bulk reconstruction [ref] , i.e., to reconstruct any operator near the brane from boundary conditions at the brane together with the bulk equations of motion.

Holographic representation of local bulk operators · RT Surfaces and Entropies in the Brane Perspective · 0.98

Cites as support 3 papers

And in fact, as discussed in [ref] this is expected.

A World without Pythons would be so Simple · Extremal Surfaces, Simple and Complex Quantities · 0.97
Lastly, recent work [ref] also indicates that this interpretation should be taken to correctly reproduce the Page curve in settings where the bath is gravitating.

An Information Paradox and Its Resolution in de Sitter Holography · RT Surfaces and Entropies in the Brane Perspective · 0.99
Lastly, recent work [ref] also indicates that this interpretation should be taken to correctly reproduce the Page curve in settings where the bath is gravitating.

Dirichlet Baths and the Not-so-Fine-Grained Page Curve · RT Surfaces and Entropies in the Brane Perspective · 0.99

Cites as background 44 papers

In the last few years it was discovered how to compute the Page curve [ref] from semi-classical gravity [ref] in a controlled manner.

Entanglement Wedge Reconstruction and the Information Paradox · Islands in Semi-Classical Gravity · 0.98
In the last few years it was discovered how to compute the Page curve [ref] from semi-classical gravity [ref] in a controlled manner.

The Page curve of Hawking radiation from semiclassical geometry · Islands in Semi-Classical Gravity · 0.98
In the last few years it was discovered how to compute the Page curve [ref] from semi-classical gravity [ref] in a controlled manner.

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole · Islands in Semi-Classical Gravity · 0.98

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