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Gravitational R\'enyi entropy from corner terms
High Energy Physics - Theory · Submitted 11 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We provide a consistent first principles prescription to compute gravitational R\'enyi entropy using Hayward corner terms.
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The abstract, sentence by sentence
We provide a consistent first principles prescription to compute gravitational R\'enyi entropy using Hayward corner terms. For Euclidean solutions to Einstein gravity, we compute R\'enyi entropy of Hartle--Hawking and fixed--area states by cutting open a manifold containing a conical singularity into a wedge with a corner. The entropy functional for fixed--area states is equal to the corner term itself, having a flat-entanglement spectrum, while extremization of the functional follows from the variation of the corner term under diffeomorphisms. Notably, our method does not require regularization of the conical singularity, and naturally extends to higher-curvature theories of gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We provide a consistent first principles prescription to compute gravitational R\'enyi entropy using Hayward corner terms. | contribution 1.00 | 0.94 | 0.68 | asserted 1.00 |
| s1 | For Euclidean solutions to Einstein gravity, we compute R\'enyi entropy of Hartle--Hawking and fixed--area states by cutting open a manifold containing a conical singularity into a wedge with a corner. | method 0.92 | 0.91 | 0.13 | asserted 1.00 |
| s2 | The entropy functional for fixed--area states is equal to the corner term itself, having a flat-entanglement spectrum, while extremization of the functional follows from the variation of the corner term under diffeomorphisms. | result 0.92 | 0.87 | 0.26 | asserted 1.00 |
| s3 | Notably, our method does not require regularization of the conical singularity, and naturally extends to higher-curvature theories of gravity. | contribution 0.49 | 0.84 | 0.14 | asserted 1.00 |
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The paper
Original abstract
We provide a consistent first principles prescription to compute gravitational R\'enyi entropy using Hayward corner terms. For Euclidean solutions to Einstein gravity, we compute R\'enyi entropy of Hartle--Hawking and fixed--area states by cutting open a manifold containing a conical singularity into a wedge with a corner. The entropy functional for fixed--area states is equal to the corner term itself, having a flat-entanglement spectrum, while extremization of the functional follows from the variation of the corner term under diffeomorphisms. Notably, our method does not require regularization of the conical singularity, and naturally extends to higher-curvature theories of gravity.
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How the literature uses it
5 arXiv papers cite this in 9 sentences
Papers citing it · 7 sentences without a confident label
Builds on it 1 paper
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This section serves as an expanded version of our previous work [ref] .
Cornering gravitational entropy · Entropy from corner terms in Einstein gravity · 0.82
Uses its method or tool 1 paper
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Explicitly, if we neglect the matter fields, the entropy evaluates to[See [ref] for more details on the evaluation of the on-shell action.] [equation] where $r$ is a local coordinate radially outward to $∂E(a)$, which is defined by $r=0$ in these coordinates.
The entropy of finite gravitating regions · The final entropy formula · 0.88
What it cites · 48 sentences without a confident label
Contests 2 papers
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The fixed-area condition was used in Fursaev's attempted proof of ([ref]) [ref] , but was shown to have a flat spectrum [ref] .
Entanglement Renyi entropies in holographic theories · Introduction · contest 0.79
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The fixed-area condition was used in Fursaev's attempted proof of ([ref]) [ref] , but was shown to have a flat spectrum [ref] .
Proof of the Holographic Formula for Entanglement Entropy · Introduction · contest 0.79
Builds on 1 paper
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Our approach thus extends these computations to backgrounds without a $U(1)$ symmetry, analogous to how [ref] generalizes the Gibbons–Hawking derivation of black hole thermodynamics [ref] .
Generalized gravitational entropy · Introduction · 0.86
Compares with 2 papers
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Second, unlike derivations [ref] , we need not regularize any conical singularity.
Generalized gravitational entropy · Introduction · 0.94
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Second, unlike derivations [ref] , we need not regularize any conical singularity.
Proof of the Holographic Formula for Entanglement Entropy · Introduction · 0.94
Cites as background 12 papers
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In practice, however, extracting the on-shell form of the subleading terms in the HH state ([ref]) for $n>1$ is non-trivial and known as the splitting problem [ref] .
Universal Terms of Entanglement Entropy for 6d CFTs · Introduction · 0.87
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In practice, however, extracting the on-shell form of the subleading terms in the HH state ([ref]) for $n>1$ is non-trivial and known as the splitting problem [ref] .
Gravity duals of boundary cones · Introduction · 0.87
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In practice, however, extracting the on-shell form of the subleading terms in the HH state ([ref]) for $n>1$ is non-trivial and known as the splitting problem [ref] .
Holographic Entanglement Entropy for the Most General Higher Derivative Gravity · Introduction · 0.87
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