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Investigations on entanglement entropy in gravity
High Energy Physics - Theory · Submitted 12 Aug 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Edge modes are conjectured to provide a statistical description of the black hole entropy, and this work takes some initial steps toward checking this conjecture in higher curvature theories.
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Entanglement entropy first arose from attempts to understand the entropy of black holes, and is believed to play a crucial role in a complete description of quantum gravity. This thesis explores some proposed connections between entanglement entropy and the geometry of spacetime. One such connection is the ability to derive gravitational field equations from entanglement identities. I will discuss a specific derivation of the Einstein equation from an equilibrium condition satisfied by entanglement entropy, and explore a subtlety in the construction when the matter fields are not conformally invariant. As a further generalization, I extend the argument to include higher curvature theories of gravity, whose consideration is necessitated by the presence of subleading divergences in the entanglement entropy beyond the area law. A deeper issue in this construction, as well as in more general considerations identifying black hole entropy with entanglement entropy, is that the entropy is ambiguous for gauge fields and gravitons. The ambiguity stems from how one handles edge modes at the entangling surface, which parameterize the gauge transformations that are broken by the presence of the boundary. The final part of this thesis is devoted to identifying the edge modes in arbitrary diffeomorphism-invariant theories. Edge modes are conjectured to provide a statistical description of the black hole entropy, and this work takes some initial steps toward checking this conjecture in higher curvature theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Entanglement entropy first arose from attempts to understand the entropy of black holes, and is believed to play a crucial role in a complete description of quantum gravity. | background 1.00 | 0.03 | 0.03 | asserted 0.55 |
| s1 | This thesis explores some proposed connections between entanglement entropy and the geometry of spacetime. | contribution 0.95 | 0.59 | 0.04 | asserted 0.73 |
| s2 | One such connection is the ability to derive gravitational field equations from entanglement identities. | background 0.58 | 0.09 | 0.09 | hedged possibility 0.51 |
| s3 | I will discuss a specific derivation of the Einstein equation from an equilibrium condition satisfied by entanglement entropy, and explore a subtlety in the construction when the matter fields are not conformally invariant. | contribution 0.98 | 0.89 | 0.13 | asserted 0.87 |
| s4 | As a further generalization, I extend the argument to include higher curvature theories of gravity, whose consideration is necessitated by the presence of subleading divergences in the entanglement entropy beyond the area law. | contribution 0.99 | 0.89 | 0.08 | asserted 0.99 |
| s5 | A deeper issue in this construction, as well as in more general considerations identifying black hole entropy with entanglement entropy, is that the entropy is ambiguous for gauge fields and gravitons. | background 0.35 | 0.14 | 0.08 | asserted 0.99 |
| s6 | The ambiguity stems from how one handles edge modes at the entangling surface, which parameterize the gauge transformations that are broken by the presence of the boundary. | background 0.88 | 0.11 | 0.04 | asserted 1.00 |
| s7 | The final part of this thesis is devoted to identifying the edge modes in arbitrary diffeomorphism-invariant theories. | contribution 0.96 | 0.67 | 0.07 | asserted 0.94 |
| s8 | Edge modes are conjectured to provide a statistical description of the black hole entropy, and this work takes some initial steps toward checking this conjecture in higher curvature theories. | contribution 0.90 | 0.71 | 0.19 | speculative 0.78 |
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Original abstract
Entanglement entropy first arose from attempts to understand the entropy of black holes, and is believed to play a crucial role in a complete description of quantum gravity. This thesis explores some proposed connections between entanglement entropy and the geometry of spacetime. One such connection is the ability to derive gravitational field equations from entanglement identities. I will discuss a specific derivation of the Einstein equation from an equilibrium condition satisfied by entanglement entropy, and explore a subtlety in the construction when the matter fields are not conformally invariant. As a further generalization, I extend the argument to include higher curvature theories of gravity, whose consideration is necessitated by the presence of subleading divergences in the entanglement entropy beyond the area law. A deeper issue in this construction, as well as in more general considerations identifying black hole entropy with entanglement entropy, is that the entropy is ambiguous for gauge fields and gravitons. The ambiguity stems from how one handles edge modes at the entangling surface, which parameterize the gauge transformations that are broken by the presence of the boundary. The final part of this thesis is devoted to identifying the edge modes in arbitrary diffeomorphism-invariant theories. Edge modes are conjectured to provide a statistical description of the black hole entropy, and this work takes some initial steps toward checking this conjecture in higher curvature theories.
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What it cites · 307 sentences without a confident label
Contests 3 papers
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However, those works did not account for the noncommutativity of the density matrix perturbation $δρ$ with the original density matrix $ρ_0$, so the results cannot be directly applied to find the finite change in entanglement entropy between the perturbed theory excited state and the CFT ground state.[However, references [ref] are able to reproduce universal logarithmic divergences when they are present. ] Instead, we will apply the technique developed by Faulkner [ref] to compute these finite changes to the entanglement entropy, which we review in section [ref].
Entanglement entropy, planar surfaces, and spectral functions · Introduction · contest 0.75
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However, those works did not account for the noncommutativity of the density matrix perturbation $δρ$ with the original density matrix $ρ_0$, so the results cannot be directly applied to find the finite change in entanglement entropy between the perturbed theory excited state and the CFT ground state.[However, references [ref] are able to reproduce universal logarithmic divergences when they are present. ] Instead, we will apply the technique developed by Faulkner [ref] to compute these finite changes to the entanglement entropy, which we review in section [ref].
Entanglement Entropy for Relevant and Geometric Perturbations · Introduction · contest 0.75
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However, those works did not account for the noncommutativity of the density matrix perturbation $δρ$ with the original density matrix $ρ_0$, so the results cannot be directly applied to find the finite change in entanglement entropy between the perturbed theory excited state and the CFT ground state.[However, references [ref] are able to reproduce universal logarithmic divergences when they are present. ] Instead, we will apply the technique developed by Faulkner [ref] to compute these finite changes to the entanglement entropy, which we review in section [ref].
Bulk Emergence and the RG Flow of Entanglement Entropy · Introduction · contest 0.75
Builds on 3 papers
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It was derived for Einstein gravity in the supplemental materials of [ref] , and one of the main results of this chapter is to extend it to arbitrary, higher derivative theories.
Entanglement Equilibrium and the Einstein Equation · Summary of results and outline · 0.99
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Building on the results of [ref] , this chapter has described a general procedure for constructing the extended phase space in a diffeomorphism-invariant theory for a local subregion.
Local subsystems in gauge theory and gravity · Discussion · 0.99
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This first law of causal diamond mechanics reads κ/8πG δA|_V+ δH_matter = 0, where $H_matter$ is the matter energy associated with translation along a conformal Killing vector that preserves the causal diamond, and $κ$ is the surface gravity of this conformal Killing vector [ref] .
Conformal Invariance of Black Hole Temperature · Gravitational dynamics from entanglement · 0.89
Uses the method or tool of 20 papers
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Chapter [ref] of this thesis is devoted to studying edge modes for arbitrary diffeomorphism-invariant theories, using the extended phase space construction of Donnelly and Freidel [ref] .
Local subsystems in gauge theory and gravity · Edge modes · 0.87
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Following the approach taken in [ref] , we employ a limit where the ball is taken to be much smaller than all relevant scales in the problem, but much larger than the cutoff scale of the effective field theory, which is set by the gravitational coupling constants.
Entanglement Equilibrium and the Einstein Equation · Field equations from the equilibrium condition · 0.91
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Faulkner has recently shown how to perform this calculation in a CFT deformed by a relevant operator, $∫f(x)(x)$ [ref] .
Bulk Emergence and the RG Flow of Entanglement Entropy · Entanglement entropy of balls in conformal perturbation theory · 0.82
Compares with 3 papers
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This subgroup was found in section [ref] to be $Diff(∂Σ)⋉(SL(2,ℝ)⋉ℝ^2·(d-2) )^∂Σ$, which is larger than the surface symmetry group $Diff(∂Σ)⋉SL(2,ℝ)^∂Σ$ found in [ref] for general relativity.
Local subsystems in gauge theory and gravity · Discussion · 0.95
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These results agree with the holographic calculations [ref] , and this chapter therefore establishes that those results extend beyond holography.
Comments on Jacobson's "Entanglement equilibrium and the Einstein equation" · Introduction · 0.80
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This expression is related to one obtained in a similar context in [ref] .
Higher-Derivative Corrections to the Asymptotic Virasoro Symmetry of 4d Extremal Black Holes · Extended phase space · 0.93
Cites as support 2 papers
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The quantum fields responsible for the entanglement entropy divergence also produce divergences that renormalize $G$, and these divergences conspire to ensure that the generalized entropy is independent of the choice of regulator [ref] .
Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory · Generalized entropy as entanglement entropy · 0.96
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A particular example is a coherent state, which has no additional entanglement entropy relative to the vacuum despite possessing energy [ref] .
A Note on Entanglement Entropy, Coherent States and Gravity · Implications for the Einstein equation · 0.99
Cites as background 37 papers
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In section [ref], we reviewed the argument that in the special case of Einstein gravity, imposing the linearized equations within small enough balls is equivalent to requiring that the fully nonlinear equations hold within the ball [ref] .
Entanglement Equilibrium and the Einstein Equation · Discussion · 0.80
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Recently, Donnelly and Freidel presented a continuum description of the edge modes that arise both in Yang-Mills theory and general relativity [ref] .
Local subsystems in gauge theory and gravity · Introduction · 0.94
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The constructions of the symplectic potential current $θ$ and Noether charge $Q_ξ$ are subject to a number of ambiguities identified by Jacobson, Kang and Myers (JKM) [ref] .
On Black Hole Entropy · JKM ambiguities · 0.90
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