CoChat
Sign Up
Cited by 30

The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.

The gravitational path integral from an observer’s point of view

Abdalla, Ahmed I., Antonini, Stefano, Iliesiu, Luca V., Levine, Adam·2025·Journal of High Energy Physics
DOI 10.1007/jhep05(2025)059
Open this paper in CoChat — free account

Abstract

A bstract: One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this paper, we develop a framework for describing non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially with $${G}_{N}^{-1}$$ . Similarly, from an observer’s perspective, the dimension of the Hilbert space in a two-sided black hole is increased. We compute various observables probing the experience of a gravitating observer in this Hilbert space. We find that an observer experiences non-trivial physics in the closed universe in contrast to what it would see in a one-dimensional Hilbert space. In the two-sided black hole setting, our proposal implies that non-perturbative corrections to effective field theory for an infalling observer are suppressed until times exponential in the black hole entropy, resolving a recently-raised puzzle in black hole physics. While the framework that we develop is exemplified in the toy-model of JT gravity, most of our analysis can be extended to higher dimensions and, in particular, to generic spacetimes not admitting a conventional holographic description, such as cosmological universes or black hole interiors.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/jhep05(2025)059

Cites

13 of 13 references verified0 citation errors · 0 not checkable

Statistics

Figures

Figure 1 Our proposal for the gravitational path integral in the presence of an observer. The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap ⟨ ψ i | ψ j ⟩ n . This rule can be seen as an additional boundary condition to impose when summing over geometries. (a) The overlap ⟨ ψ i | ψ j ⟩ between two closed universe states in pure JT gravity is unaffected by our new rules. (b) The square of an overlap |⟨ ψ i | ψ j ⟩| 2 between closed universe states. The gravitational path integral sums over all possible geometries satisfying the boundary conditions at the asymptotic boundaries and at the worldline of the observer. We depict here the leading disconnected contribution and the first subleading term, a genus-zero connected geometry.
Figure 1 Our proposal for the gravitational path integral in the presence of an observer. The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap ⟨ ψ i | ψ j ⟩ n . This rule can be seen as an additional boundary condition to impose when summing over geometries. (a) The overlap ⟨ ψ i | ψ j ⟩ between two closed universe states in pure JT gravity is unaffected by our new rules. (b) The square of an overlap |⟨ ψ i | ψ j ⟩| 2 between closed universe states. The gravitational path integral sums over all possible geometries satisfying the boundary conditions at the asymptotic boundaries and at the worldline of the observer. We depict here the leading disconnected contribution and the first subleading term, a genus-zero connected geometry.CC-BY · From the PDF
Image 2
CC-BY · From the PDF
Image 3
CC-BY · From the PDF
Figure 2 (Left) A Lorentzian Big Bang-Big Crunch closed universe with a Cauchy slice of maximal length b (depicted in blue). (Right) Its Euclidean counterpart has two AdS asymptotic boundaries connected by a Euclidean wormhole. The geodesic slice of minimal length b is identical to the maximal slice in Lorentzian signature. This length is vanishingly small on-shell when the wormhole is not supported by matter and is finite in the presence of matter.
Figure 2 (Left) A Lorentzian Big Bang-Big Crunch closed universe with a Cauchy slice of maximal length b (depicted in blue). (Right) Its Euclidean counterpart has two AdS asymptotic boundaries connected by a Euclidean wormhole. The geodesic slice of minimal length b is identical to the maximal slice in Lorentzian signature. This length is vanishingly small on-shell when the wormhole is not supported by matter and is finite in the presence of matter.CC-BY · From the PDF
Image 5
CC-BY · From the PDF
Image 6
CC-BY · From the PDF
Image 7
CC-BY · From the PDF
Figure 3 The integration contour needed to calculate the Hilbert space dimension consists of the large defining contour of the resolvent C ∞ and a small contour C 0 used to exclude the contributions from zero eigenvalues of the Gram matrix.
Figure 3 The integration contour needed to calculate the Hilbert space dimension consists of the large defining contour of the resolvent C ∞ and a small contour C 0 used to exclude the contributions from zero eigenvalues of the Gram matrix.CC-BY · From the PDF
Image 9
CC-BY · From the PDF
Image 10
CC-BY · From the PDF
Image 11
CC-BY · From the PDF
Image 12
CC-BY · From the PDF
Image 13
CC-BY · From the PDF
Image 14
CC-BY · From the PDF
Figure 4 Overlap between an asymptotic closed universe state | β, ∆ ( i ) O ⟩ and a state defined on the closed minimal geodesic (depicted in green) | b, ∆ ( i ) O , u ⟩ . Left: the overlap on the Euclidean cylinder. The state on the minimal closed geodesic is labeled by the length b of the closed minimal geodesic and the length u of a geodesic segment wrapping the cylinder once and intersecting the observer's worldline perpendicularly at both ends. Right: the cylinder can be cut along the observer's worldline and embedded in the Poincar´ e disk (depicted in black), with the two red lines identified. The contribution of this geometry to the path integral can be decomposed into a Hartle-Hawking wavefunction ϕ β ( ℓ i ), with ℓ i the length of a geodesic starting and ending at the insertion of the observer on the asymptotic boundary, and a quadrilateral.
Figure 4 Overlap between an asymptotic closed universe state | β, ∆ ( i ) O ⟩ and a state defined on the closed minimal geodesic (depicted in green) | b, ∆ ( i ) O , u ⟩ . Left: the overlap on the Euclidean cylinder. The state on the minimal closed geodesic is labeled by the length b of the closed minimal geodesic and the length u of a geodesic segment wrapping the cylinder once and intersecting the observer's worldline perpendicularly at both ends. Right: the cylinder can be cut along the observer's worldline and embedded in the Poincar´ e disk (depicted in black), with the two red lines identified. The contribution of this geometry to the path integral can be decomposed into a Hartle-Hawking wavefunction ϕ β ( ℓ i ), with ℓ i the length of a geodesic starting and ending at the insertion of the observer on the asymptotic boundary, and a quadrilateral.CC-BY · From the PDF
Figure 5 Non-perturbative corrections to the overlap ⟨ b, ∆ ( i ) O , u | β, ∆ ( j ) O ⟩ . The geodesic slice of length b is depicted in green. Any higher-genus geometry contributing to the overlap can be decomposed into a genus-zero quadrilateral similar to Figure 4 and a region with a higher genus homologous to the boundary. The contribution of geometries with higher topology is then encoded in the Hartle-Hawking wavefunction.
Figure 5 Non-perturbative corrections to the overlap ⟨ b, ∆ ( i ) O , u | β, ∆ ( j ) O ⟩ . The geodesic slice of length b is depicted in green. Any higher-genus geometry contributing to the overlap can be decomposed into a genus-zero quadrilateral similar to Figure 4 and a region with a higher genus homologous to the boundary. The contribution of geometries with higher topology is then encoded in the Hartle-Hawking wavefunction.CC-BY · From the PDF
Image 17
CC-BY · From the PDF
Figure 7 Path integral preparing a generic closed universe state | ψ i ⟩ in the presence of an observer and a matter insertion labeled by i . Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of a matter operator with flavor i and scaling dimension ∆ m at the asymptotic boundary. The insertions are at antipodal points. Right: the gravitational path integral prepares a state for the closed universe satisfying these boundary conditions. We indicate here the energies s 1 and s 2 of the patches to the left and right of the observer. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.1) and (4.2).
Figure 7 Path integral preparing a generic closed universe state | ψ i ⟩ in the presence of an observer and a matter insertion labeled by i . Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of a matter operator with flavor i and scaling dimension ∆ m at the asymptotic boundary. The insertions are at antipodal points. Right: the gravitational path integral prepares a state for the closed universe satisfying these boundary conditions. We indicate here the energies s 1 and s 2 of the patches to the left and right of the observer. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.1) and (4.2).CC-BY · From the PDF
Figure 8 Genus-zero pinwheel geometry contributing to the n = 3 moment of an overlap ⟨ ψ i | ψ j ⟩⟨ ψ j | ψ k ⟩⟨ ψ k | ψ i ⟩ (no sum over indices). The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets.
Figure 8 Genus-zero pinwheel geometry contributing to the n = 3 moment of an overlap ⟨ ψ i | ψ j ⟩⟨ ψ j | ψ k ⟩⟨ ψ k | ψ i ⟩ (no sum over indices). The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets.CC-BY · From the PDF
Image 20
CC-BY · From the PDF
Figure 9 Path integral preparing a state | ψ ii ′ ⟩ for the two-sided black hole in the presence of an observer and matter insertions to the right and left of the observer labeled by i and i ′ . Every boundary segment in the preparation of a state is taken to have length β/ 8. Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of matter operators with flavors i and i ′ and scaling dimension ∆ m at the asymptotic boundary. Right: the gravitational path integral prepares a state for the two-sided black hole satisfying these boundary conditions. We indicate here the energies s 1 , s 2 , s 3 , s 4 of the four patches. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.11) and (4.12).
Figure 9 Path integral preparing a state | ψ ii ′ ⟩ for the two-sided black hole in the presence of an observer and matter insertions to the right and left of the observer labeled by i and i ′ . Every boundary segment in the preparation of a state is taken to have length β/ 8. Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of matter operators with flavors i and i ′ and scaling dimension ∆ m at the asymptotic boundary. Right: the gravitational path integral prepares a state for the two-sided black hole satisfying these boundary conditions. We indicate here the energies s 1 , s 2 , s 3 , s 4 of the four patches. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.11) and (4.12).CC-BY · From the PDF
Figure 10 Genus n -1 geometries with n boundaries contributing to the n -th moment of an overlap in the two-sided black hole in the presence of an observer. The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets. Geodesics do not intersect in these leading, connected contributions. (a) Genus g = 1, 2-boundary geometry contributing to the square of an overlap |⟨ ψ jj ′ | ψ ii ′ ⟩| 2 . (b) Genus g = 2, 3-boundary geometry contributing to the n = 3 moment of an overlap ⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | ψ kk ′ ⟩⟨ ψ kk ′ | ψ jj ′ ⟩ (no sum over indices).
Figure 10 Genus n -1 geometries with n boundaries contributing to the n -th moment of an overlap in the two-sided black hole in the presence of an observer. The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets. Geodesics do not intersect in these leading, connected contributions. (a) Genus g = 1, 2-boundary geometry contributing to the square of an overlap |⟨ ψ jj ′ | ψ ii ′ ⟩| 2 . (b) Genus g = 2, 3-boundary geometry contributing to the n = 3 moment of an overlap ⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | ψ kk ′ ⟩⟨ ψ kk ′ | ψ jj ′ ⟩ (no sum over indices).CC-BY · From the PDF
Figure 11 The genus n -1, n -boundary geometry contributing to the n -th moment of an overlap can be obtained by gluing together two genus-0 pinwheel geometries with n boundaries. Here we depict the pinwheels and the resulting glued geometry for n = 3. Each boundary of the pinwheels is composed of a segment of asymptotic boundary and a segment of observer's worldline. The two pinwheels are glued together along the observer's worldlines as depicted.
Figure 11 The genus n -1, n -boundary geometry contributing to the n -th moment of an overlap can be obtained by gluing together two genus-0 pinwheel geometries with n boundaries. Here we depict the pinwheels and the resulting glued geometry for n = 3. Each boundary of the pinwheels is composed of a segment of asymptotic boundary and a segment of observer's worldline. The two pinwheels are glued together along the observer's worldlines as depicted.CC-BY · From the PDF
Image 24
CC-BY · From the PDF
Figure 12 Euclidean diagrams showing the two-point function of a scalar field ϕ , dressed to the worldline of the observer. The figure on the right is obtained by cutting the figure on the left along the observer's worldline, embedding the resulting geometry in the Poincar´ e disk (depicted in black), and then identifying the two red geodesics of length ℓ in the right diagram. We give an example of the worldline connecting the two operator insertions that winds once around the cylinder, which we show in dark green in both diagrams. The light green circle (left) and line (right) represent the shortest closed geodesic on the geometry, while the blue line (only shown on the right) is the shortest geodesic (not closed) perpendicular to the worldline of the observer on both ends. To evaluate the two-point function in the Lorentzian closed universe we perform the analytic continuation τ 1 , 2 = -it 1 , 2 .
Figure 12 Euclidean diagrams showing the two-point function of a scalar field ϕ , dressed to the worldline of the observer. The figure on the right is obtained by cutting the figure on the left along the observer's worldline, embedding the resulting geometry in the Poincar´ e disk (depicted in black), and then identifying the two red geodesics of length ℓ in the right diagram. We give an example of the worldline connecting the two operator insertions that winds once around the cylinder, which we show in dark green in both diagrams. The light green circle (left) and line (right) represent the shortest closed geodesic on the geometry, while the blue line (only shown on the right) is the shortest geodesic (not closed) perpendicular to the worldline of the observer on both ends. To evaluate the two-point function in the Lorentzian closed universe we perform the analytic continuation τ 1 , 2 = -it 1 , 2 .CC-BY · From the PDF
Figure 13 Two frontal views of the closed universe in Lorentzian signature. The observer's worldline is depicted in red and the maximal Cauchy slice of length b is depicted in green. We insert a matter insertion at time t 1 = 0, defined by where the observer intersects this Cauchy slice. Another matter insertion is place sometime later along the observer's worldline. ( Left ) Left and right null rays emanating from the first matter insertion are shown in brown. Each time the second operator insertion is placed at the intersection of these null rays with the worldline of the observer, the two-point function on a fixed background diverges. ( Right ) Generically, an infinite number of winding geodesics contribute to the twopoint function. A timelike geodesic along the observer's worldline is drawn in purple, a winding spacelike geodesic is drawn in blue, and a null winding geodesic is shown in brown.
Figure 13 Two frontal views of the closed universe in Lorentzian signature. The observer's worldline is depicted in red and the maximal Cauchy slice of length b is depicted in green. We insert a matter insertion at time t 1 = 0, defined by where the observer intersects this Cauchy slice. Another matter insertion is place sometime later along the observer's worldline. ( Left ) Left and right null rays emanating from the first matter insertion are shown in brown. Each time the second operator insertion is placed at the intersection of these null rays with the worldline of the observer, the two-point function on a fixed background diverges. ( Right ) Generically, an infinite number of winding geodesics contribute to the twopoint function. A timelike geodesic along the observer's worldline is drawn in purple, a winding spacelike geodesic is drawn in blue, and a null winding geodesic is shown in brown.CC-BY · From the PDF
Figure 14 The left-most diagram illustrates how if the observer and particle jump in both at early times, the geodesic slice for the wormhole is shrinking. This leads to a large relative boost between the observer and the particle and a correspondingly high energy collision. If both insertions happen far in the future (center diagram), then the observer and particle experience a growing wormhole length and only a minor collision. In the right-most diagram, we illustrate how the boost symmetry of the thermofield double can be used to move one of the insertions down to T = 0. In this work we choose to fix V at T = 0 on the left and vary the time that the observer jumps in. The above figure is reproduced from Figure 1 of [38].
Figure 14 The left-most diagram illustrates how if the observer and particle jump in both at early times, the geodesic slice for the wormhole is shrinking. This leads to a large relative boost between the observer and the particle and a correspondingly high energy collision. If both insertions happen far in the future (center diagram), then the observer and particle experience a growing wormhole length and only a minor collision. In the right-most diagram, we illustrate how the boost symmetry of the thermofield double can be used to move one of the insertions down to T = 0. In this work we choose to fix V at T = 0 on the left and vary the time that the observer jumps in. The above figure is reproduced from Figure 1 of [38].CC-BY · From the PDF
Image 28
CC-BY · From the PDF
Image 29
CC-BY · From the PDF
Image 30
CC-BY · From the PDF
Figure 15 The left figure illustrates the geometry obtained upon cutting the wormhole in (6.36) along the dashed line. The resulting geometry corresponds to the bra-ket to bra-ket wormhole contributing to the square of ⟨ n, s L , s R | V (0) O O ( -T ) ⟩ . In the right figure, the | n, s L , s R ⟩ boundary conditions are replaced by (an integral of) asymptotic boundary segments given by the state | s L , s R , V O O s ⟩ .
Figure 15 The left figure illustrates the geometry obtained upon cutting the wormhole in (6.36) along the dashed line. The resulting geometry corresponds to the bra-ket to bra-ket wormhole contributing to the square of ⟨ n, s L , s R | V (0) O O ( -T ) ⟩ . In the right figure, the | n, s L , s R ⟩ boundary conditions are replaced by (an integral of) asymptotic boundary segments given by the state | s L , s R , V O O s ⟩ .CC-BY · From the PDF
Image 32
CC-BY · From the PDF
Image 33
CC-BY · From the PDF
Image 34
CC-BY · From the PDF
Figure 16 Examples of two-dimensional boundary configurations relevant for studying dressed observables in a closed universe (left figures) or in a two-sided black hole (right figures). The undeformed CFT is placed on all tori (asymptotic boundaries); a future task is to find the precise deformation of the CFT to be placed on the red cylinders (boundaries of the observer worldvolumes). The first figure in each set assumes that the worldvolume of each observer is bounded by the thin red cylinder, while the second figure in each set assumes that the observer is circularly symmetric and their worldvolume is bounded by the two red cylinders. The latter case is related through dimensional reduction to the analysis performed in this paper.
Figure 16 Examples of two-dimensional boundary configurations relevant for studying dressed observables in a closed universe (left figures) or in a two-sided black hole (right figures). The undeformed CFT is placed on all tori (asymptotic boundaries); a future task is to find the precise deformation of the CFT to be placed on the red cylinders (boundaries of the observer worldvolumes). The first figure in each set assumes that the worldvolume of each observer is bounded by the thin red cylinder, while the second figure in each set assumes that the observer is circularly symmetric and their worldvolume is bounded by the two red cylinders. The latter case is related through dimensional reduction to the analysis performed in this paper.CC-BY · From the PDF
Figure 17 The Euclidean preparation (bottom half) and subsequent Lorentzian evolution (top half) of a de Sitter state | a, K, ∆ ( i ) O ⟩ specified by the length a and extrinsic curvature K of an initial slice at Euclidean time τ = τ i where the observer is inserted. The Lorentzian part of the evolution from the Euclidean sphere's equator at τ = 0 (depicted in blue) yields Lorentzian dS 2 , with a spacelike asymptotic boundary at Lorentzian time t → ∞ . Our set of states | a, K, ∆ ( i ) O ⟩ includes (but is not limited to) the smooth Hartle-Hawking no-boundary state.
Figure 17 The Euclidean preparation (bottom half) and subsequent Lorentzian evolution (top half) of a de Sitter state | a, K, ∆ ( i ) O ⟩ specified by the length a and extrinsic curvature K of an initial slice at Euclidean time τ = τ i where the observer is inserted. The Lorentzian part of the evolution from the Euclidean sphere's equator at τ = 0 (depicted in blue) yields Lorentzian dS 2 , with a spacelike asymptotic boundary at Lorentzian time t → ∞ . Our set of states | a, K, ∆ ( i ) O ⟩ includes (but is not limited to) the smooth Hartle-Hawking no-boundary state.CC-BY · From the PDF
Figure 18 The gravitational path integral in the presence of an observer for de Sitter spacetime. A state is defined in terms of the length a and extrinsic curvature K of an initial slice where we insert the observer with scaling dimension ∆ O . The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap. (a) The overlap ⟨ a ′ , K ′ | a, K ⟩ between two states. (b) The square of an overlap |⟨ a ′ , K ′ | a, K ⟩| 2 in the presence of an observer. The variance of the overlap is given by the connected geometry on the right, namely a sphere with four holes, and is therefore O ( e -2 S 0 ). This suggests a Hilbert space dimension dim ( H rel non-pert ) = O ( e 2 S 0 ). We plan to explicitly compute this dimension in future work.
Figure 18 The gravitational path integral in the presence of an observer for de Sitter spacetime. A state is defined in terms of the length a and extrinsic curvature K of an initial slice where we insert the observer with scaling dimension ∆ O . The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap. (a) The overlap ⟨ a ′ , K ′ | a, K ⟩ between two states. (b) The square of an overlap |⟨ a ′ , K ′ | a, K ⟩| 2 in the presence of an observer. The variance of the overlap is given by the connected geometry on the right, namely a sphere with four holes, and is therefore O ( e -2 S 0 ). This suggests a Hilbert space dimension dim ( H rel non-pert ) = O ( e 2 S 0 ). We plan to explicitly compute this dimension in future work.CC-BY · From the PDF
Image 38
CC-BY · From the PDF
Image 39
CC-BY · From the PDF
Image 40
CC-BY · From the PDF
Image 41
CC-BY · From the PDF
Figure 19 Boundary conditions for a closed universe state prepared by the insertion of the observer, a matter operator of flavor i , and operators k l = e -β l H l and k r = e -β r H r to the left and right of the observer. The insertion of k l and k r in a state with boundary length β/ 2 to the left and right of the observer (left picture) is equivalent to a state with boundary length β/ 2 + β l to the left of the observer and β/ 2 + β r to the right of the observer (right picture).
Figure 19 Boundary conditions for a closed universe state prepared by the insertion of the observer, a matter operator of flavor i , and operators k l = e -β l H l and k r = e -β r H r to the left and right of the observer. The insertion of k l and k r in a state with boundary length β/ 2 to the left and right of the observer (left picture) is equivalent to a state with boundary length β/ 2 + β l to the left of the observer and β/ 2 + β r to the right of the observer (right picture).CC-BY · From the PDF
Figure 20 Genus-zero pinwheel geometry contributing to the n = 2 term ⟨ ψ l | ψ i ⟩⟨ ψ i | ψ j ⟩⟨ ψ j | k l k r | ψ l ⟩ on the right hand side of equation (C.4).
Figure 20 Genus-zero pinwheel geometry contributing to the n = 2 term ⟨ ψ l | ψ i ⟩⟨ ψ i | ψ j ⟩⟨ ψ j | k l k r | ψ l ⟩ on the right hand side of equation (C.4).CC-BY · From the PDF
Figure 21 Boundary conditions for a two-sided black hole state prepared by the insertion of the observer, two matter operators to the left and right of the observer, and operators k l = e -β l H l , k r = e -β r H r , k L = e -β L H L , k R = e -β R H R . The insertion of k l , k r , k L , k R in a state with every boundary segment of length β/ 8 (left picture) is equivalent to a state with boundary segments of length β/ 8 + β l , β/ 8 + β r , β/ 8 + β L , and β/ 8 + β R (right picture).
Figure 21 Boundary conditions for a two-sided black hole state prepared by the insertion of the observer, two matter operators to the left and right of the observer, and operators k l = e -β l H l , k r = e -β r H r , k L = e -β L H L , k R = e -β R H R . The insertion of k l , k r , k L , k R in a state with every boundary segment of length β/ 8 (left picture) is equivalent to a state with boundary segments of length β/ 8 + β l , β/ 8 + β r , β/ 8 + β L , and β/ 8 + β R (right picture).CC-BY · From the PDF
Figure 22 Genus g = 2 geometry contributing to the n = 2 term ⟨ ψ ll ′ | ψ jj ′ ⟩⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | k L k l k R k r | ψ ll ′ ⟩ on the right hand side of equation (C.13).
Figure 22 Genus g = 2 geometry contributing to the n = 2 term ⟨ ψ ll ′ | ψ jj ′ ⟩⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | k L k l k R k r | ψ ll ′ ⟩ on the right hand side of equation (C.13).CC-BY · From the PDF

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Research works printed but not linked: 118

  1. L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE]. · DOI · Paper page
  2. G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE]. · arXiv
  3. J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE]. · DOI · Paper page
  4. E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE]. · DOI · Paper page
  5. O. Aharony et al., Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE]. · DOI
  6. G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE]. · DOI · Paper page
  7. J.M. Maldacena and L. Maoz, Wormholes in AdS, JHEP 02 (2004) 053 [hep-th/0401024] [INSPIRE]. · DOI · Paper page
  8. A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE]. · DOI · Paper page
  9. T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE]. · DOI · Paper page
  10. P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE]. · arXiv
  11. P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE]. · arXiv
  12. P. Saad, S.H. Shenker, D. Stanford and S. Yao, Wormholes without averaging, JHEP 09 (2024) 133 [arXiv:2103.16754] [INSPIRE]. · DOI · Paper page
  13. P. Saad, S.H. Shenker and S. Yao, Comments on wormholes and factorization, JHEP 10 (2024) 076 [arXiv:2107.13130] [INSPIRE]. · DOI
  14. A. Blommaert, L.V. Iliesiu and J. Kruthoff, Gravity factorized, JHEP 09 (2022) 080 [arXiv:2111.07863] [INSPIRE]. · DOI
  15. A. Blommaert, L.V. Iliesiu and J. Kruthoff, Alpha states demystified — towards microscopic models of AdS2 holography, JHEP 08 (2022) 071 [arXiv:2203.07384] [INSPIRE]. · DOI
  16. J. Boruch, L.V. Iliesiu and C. Yan, Constructing all BPS black hole microstates from the gravitational path integral, JHEP 09 (2024) 058 [arXiv:2307.13051] [INSPIRE]. · DOI
  17. L.V. Iliesiu, M. Kologlu and G.J. Turiaci, Supersymmetric indices factorize, JHEP 05 (2023) 032 [arXiv:2107.09062] [INSPIRE]. · DOI · Paper page
  18. L.V. Iliesiu, S. Murthy and G.J. Turiaci, Black hole microstate counting from the gravitational path integral, arXiv:2209.13602 [INSPIRE]. · arXiv
  19. D. Marolf, Gravitational thermodynamics without the conformal factor problem: partition functions and Euclidean saddles from Lorentzian path integrals, JHEP 07 (2022) 108 [arXiv:2203.07421] [INSPIRE]. · DOI
  20. E. Colafranceschi, X. Dong, D. Marolf and Z. Wang, Algebras and Hilbert spaces from gravitational path integrals. Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT, JHEP 10 (2024) 063 [arXiv:2310.02189] [INSPIRE]. · DOI
  21. D. Marolf, On the nature of ensembles from gravitational path integrals, J. Phys. A 58 (2025) 035204 [arXiv:2407.04625] [INSPIRE]. · DOI
  22. V. Balasubramanian, A. Lawrence, J.M. Magan and M. Sasieta, Microscopic Origin of the Entropy of Black Holes in General Relativity, Phys. Rev. X 14 (2024) 011024 [arXiv:2212.02447] [INSPIRE]. · arXiv
  23. V. Balasubramanian, A. Lawrence, J.M. Magan and M. Sasieta, Microscopic Origin of the Entropy of Astrophysical Black Holes, Phys. Rev. Lett. 132 (2024) 141501 [arXiv:2212.08623] [INSPIRE]. · DOI
  24. M. Sasieta, Wormholes from heavy operator statistics in AdS/CFT, JHEP 03 (2023) 158 [arXiv:2211.11794] [INSPIRE]. · DOI · Paper page
  25. S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE]. · DOI · Paper page
  26. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE]. · DOI · Paper page
  27. N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE]. · DOI · Paper page
  28. L. Susskind, Singularities, Firewalls, and Complementarity, arXiv:1208.3445 [INSPIRE]. · arXiv
  29. A. Almheiri et al., An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE]. · DOI · Paper page
  30. D. Stanford and Z. Yang, Firewalls from wormholes, arXiv:2208.01625 [INSPIRE]. · arXiv
  31. L.V. Iliesiu et al., On the non-perturbative bulk Hilbert space of JT gravity, JHEP 10 (2024) 220 [arXiv:2403.08696] [INSPIRE]. · DOI
  32. A. Blommaert, C.-H. Chen and Y. Nomura, Firewalls at exponentially late times, JHEP 10 (2024) 131 [arXiv:2403.07049] [INSPIRE]. · DOI
  33. A. Levine and E. Shaghoulian, Encoding beyond cosmological horizons in de Sitter JT gravity, JHEP 02 (2023) 179 [arXiv:2204.08503] [INSPIRE]. · DOI
  34. B. McInnes, Answering a basic objection to bang / crunch holography, JHEP 10 (2004) 018 [hep-th/0407189] [INSPIRE]. · DOI
  35. S. Cooper et al., Black hole microstate cosmology, JHEP 07 (2019) 065 [arXiv:1810.10601] [INSPIRE]. · DOI
  36. S. Antonini and B. Swingle, Cosmology at the end of the world, Nature Phys. 16 (2020) 881 [arXiv:1907.06667] [INSPIRE]. · DOI
  37. M. Van Raamsdonk, Comments on wormholes, ensembles, and cosmology, JHEP 12 (2021) 156 [arXiv:2008.02259] [INSPIRE]. · DOI
  38. M. Van Raamsdonk, Cosmology from confinement?, JHEP 03 (2022) 039 [arXiv:2102.05057] [INSPIRE]. · DOI
  39. S. Antonini, P. Simidzija, B. Swingle and M. Van Raamsdonk, Cosmology from the vacuum, Class. Quant. Grav. 41 (2024) 045008 [arXiv:2203.11220] [INSPIRE]. · DOI
  40. S. Antonini, P. Simidzija, B. Swingle and M. Van Raamsdonk, Accelerating Cosmology from a Holographic Wormhole, Phys. Rev. Lett. 130 (2023) 221601 [arXiv:2206.14821] [INSPIRE]. · DOI
  41. S. Antonini et al., Accelerating cosmology from Λ < 0 gravitational effective field theory, JHEP 05 (2023) 203 [arXiv:2212.00050] [INSPIRE]. · DOI
  42. A. Sahu, P. Simidzija and M. Van Raamsdonk, Bubbles of cosmology in AdS/CFT, JHEP 11 (2023) 010 [arXiv:2306.13143] [INSPIRE]. · DOI
  43. J. Chakravarty, A. Maloney, K. Namjou and S.F. Ross, A new observable for holographic cosmology, JHEP 10 (2024) 184 [arXiv:2407.04781] [INSPIRE]. · DOI
  44. S. Antonini and L.G.C. Bariuan, Magnetic braneworlds: cosmology and wormholes, JHEP 09 (2024) 070 [arXiv:2405.18465] [INSPIRE]. · DOI
  45. P. Betzios and O. Papadoulaki, Inflationary Cosmology from Anti-de Sitter Wormholes, Phys. Rev. Lett. 133 (2024) 021501 [arXiv:2403.17046] [INSPIRE]. · DOI
  46. M. Van Raamsdonk and C. Waddell, Holographic motivations and observational evidence for decreasing dark energy, arXiv:2406.02688 [INSPIRE]. · arXiv
  47. S. Antonini and P. Rath, Do holographic CFT states have unique semiclassical bulk duals?, arXiv:2408.02720 [INSPIRE]. · arXiv
  48. A. Sahu and M. Van Raamsdonk, Holographic black hole cosmologies, arXiv:2411.14673 [INSPIRE]. · arXiv
  49. V. Chandrasekaran, R. Longo, G. Penington and E. Witten, An algebra of observables for de Sitter space, JHEP 02 (2023) 082 [arXiv:2206.10780] [INSPIRE]. · DOI
  50. A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE]. · DOI
  51. E. Coleman et al., De Sitter microstates from $$T\overline{T }$$ + Λ2 and the Hawking-Page transition, JHEP 07 (2022) 140 [arXiv:2110.14670] [INSPIRE]. · DOI
  52. X. Dong, E. Silverstein and G. Torroba, De Sitter Holography and Entanglement Entropy, JHEP 07 (2018) 050 [arXiv:1804.08623] [INSPIRE]. · DOI · Paper page
  53. G. Araujo-Regado, R. Khan and A.C. Wall, Cauchy slice holography: a new AdS/CFT dictionary, JHEP 03 (2023) 026 [arXiv:2204.00591] [INSPIRE]. · DOI
  54. P. McFadden and K. Skenderis, Holography for Cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [INSPIRE]. · DOI
  55. D. Anninos, S.A. Hartnoll and D.M. Hofman, Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline, Class. Quant. Grav. 29 (2012) 075002 [arXiv:1109.4942] [INSPIRE]. · DOI
  56. D. Anninos, T. Anous, I. Bredberg and G.S. Ng, Incompressible Fluids of the de Sitter Horizon and Beyond, JHEP 05 (2012) 107 [arXiv:1110.3792] [INSPIRE]. · DOI
  57. S. Leutheusser and H. Liu, Subregion-subalgebra duality: Emergence of space and time in holography, Phys. Rev. D 111 (2025) 066021 [arXiv:2212.13266] [INSPIRE]. · DOI
  58. E. Witten, Gravity and the crossed product, JHEP 10 (2022) 008 [arXiv:2112.12828] [INSPIRE]. · DOI
  59. V. Chandrasekaran, G. Penington and E. Witten, Large N algebras and generalized entropy, JHEP 04 (2023) 009 [arXiv:2209.10454] [INSPIRE]. · DOI
  60. E. Witten, Algebras, regions, and observers, Proc. Symp. Pure Math. 107 (2024) 247 [arXiv:2303.02837] [INSPIRE]. · arXiv
  61. E. Witten, A background-independent algebra in quantum gravity, JHEP 03 (2024) 077 [arXiv:2308.03663] [INSPIRE]. · DOI
  62. E. Gesteau, Large N von Neumann Algebras and the Renormalization of Newton’s Constant, Commun. Math. Phys. 406 (2025) 40 [arXiv:2302.01938] [INSPIRE]. · DOI
  63. D.K. Kolchmeyer and H. Liu, Chaos and the Emergence of the Cosmological Horizon, arXiv:2411.08090 [INSPIRE]. · arXiv
  64. C.-H. Chen and G. Penington, A clock is just a way to tell the time: gravitational algebras in cosmological spacetimes, arXiv:2406.02116 [INSPIRE]. · arXiv
  65. J. Kudler-Flam, S. Leutheusser and G. Satishchandran, Algebraic Observational Cosmology, arXiv:2406.01669 [INSPIRE]. · arXiv
  66. J. De Vuyst, S. Eccles, P.A. Hoehn and J. Kirklin, Gravitational entropy is observer-dependent, arXiv:2405.00114 [INSPIRE]. · arXiv
  67. J. Boruch, L.V. Iliesiu, G. Lin and C. Yan, How the Hilbert space of two-sided black holes factorises, arXiv:2406.04396 [INSPIRE]. · arXiv
  68. S. Antonini, M. Sasieta and B. Swingle, Cosmology from random entanglement, JHEP 11 (2023) 188 [arXiv:2307.14416] [INSPIRE]. · DOI · Paper page
  69. M. Usatyuk, Z.-Y. Wang and Y. Zhao, Closed universes in two dimensional gravity, SciPost Phys. 17 (2024) 051 [arXiv:2402.00098] [INSPIRE]. · DOI
  70. M. Usatyuk and Y. Zhao, Closed universes, factorization, and ensemble averaging, JHEP 02 (2025) 052 [arXiv:2403.13047] [INSPIRE]. · DOI
  71. E. Di Valentino, A. Melchiorri and J. Silk, Planck evidence for a closed Universe and a possible crisis for cosmology, Nature Astron. 4 (2019) 196 [arXiv:1911.02087] [INSPIRE]. · DOI · Paper page
  72. W. Handley, Curvature tension: evidence for a closed universe, Phys. Rev. D 103 (2021) L041301 [arXiv:1908.09139] [INSPIRE]. · DOI · Paper page
  73. Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE]. · arXiv
  74. R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE]. · DOI · Paper page
  75. C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE]. · DOI · Paper page
  76. P.-S. Hsin, L.V. Iliesiu and Z. Yang, A violation of global symmetries from replica wormholes and the fate of black hole remnants, Class. Quant. Grav. 38 (2021) 194004 [arXiv:2011.09444] [INSPIRE]. · DOI
  77. C. Akers and G. Penington, Quantum minimal surfaces from quantum error correction, SciPost Phys. 12 (2022) 157 [arXiv:2109.14618] [INSPIRE]. · DOI · Paper page
  78. C. Akers et al., The black hole interior from non-isometric codes and complexity, JHEP 06 (2024) 155 [arXiv:2207.06536] [INSPIRE]. · DOI · Paper page
  79. S. Antonini et al., Non-isometry, state dependence and holography, JHEP 02 (2025) 150 [arXiv:2411.07296] [INSPIRE]. · DOI · Paper page
  80. T. Hartman, Y. Jiang and E. Shaghoulian, Islands in cosmology, JHEP 11 (2020) 111 [arXiv:2008.01022] [INSPIRE]. · DOI
  81. D. Marolf and J. Polchinski, Violations of the Born rule in cool state-dependent horizons, JHEP 01 (2016) 008 [arXiv:1506.01337] [INSPIRE]. · DOI
  82. D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE]. · DOI
  83. D. Harlow and D. Jafferis, The Factorization Problem in Jackiw-Teitelboim Gravity, JHEP 02 (2020) 177 [arXiv:1804.01081] [INSPIRE]. · DOI · Paper page
  84. G. Penington and E. Witten, Algebras and States in JT Gravity, arXiv:2301.07257 [INSPIRE]. · arXiv
  85. D.K. Kolchmeyer, von Neumann algebras in JT gravity, JHEP 06 (2023) 067 [arXiv:2303.04701] [INSPIRE]. · DOI
  86. Z. Yang, The Quantum Gravity Dynamics of Near Extremal Black Holes, JHEP 05 (2019) 205 [arXiv:1809.08647] [INSPIRE]. · DOI · Paper page
  87. A. Kitaev and S.J. Suh, Statistical mechanics of a two-dimensional black hole, JHEP 05 (2019) 198 [arXiv:1808.07032] [INSPIRE]. · DOI · Paper page
  88. C.J. Isham, Canonical quantum gravity and the problem of time, NATO Sci. Ser. C 409 (1993) 157 [gr-qc/9210011] [INSPIRE]. · DOI
  89. J. Held and H. Maxfield, The Hilbert space of de Sitter JT: a case study for canonical methods in quantum gravity, arXiv:2410.14824 [INSPIRE]. · arXiv
  90. D.L. Jafferis, D.K. Kolchmeyer, B. Mukhametzhanov and J. Sonner, Jackiw-Teitelboim gravity with matter, generalized eigenstate thermalization hypothesis, and random matrices, Phys. Rev. D 108 (2023) 066015 [arXiv:2209.02131] [INSPIRE]. · DOI
  91. D. Stanford and E. Witten, JT gravity and the ensembles of random matrix theory, Adv. Theor. Math. Phys. 24 (2020) 1475 [arXiv:1907.03363] [INSPIRE]. · DOI · Paper page
  92. L.V. Iliesiu, M. Mezei and G. Sárosi, The volume of the black hole interior at late times, JHEP 07 (2022) 073 [arXiv:2107.06286] [INSPIRE]. · DOI · Paper page
  93. Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitationally prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE]. · DOI
  94. C. Akers, A. Levine, G. Penington and E. Wildenhain, One-shot holography, SciPost Phys. 16 (2024) 144 [arXiv:2307.13032] [INSPIRE]. · DOI
  95. E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2001), Boulder, CO, U.S.A., 3–29 June 2001 [hep-th/0201253] [INSPIRE]. · arXiv
  96. L. Susskind, The Typical-State Paradox: Diagnosing Horizons with Complexity, Fortsch. Phys. 64 (2016) 84 [arXiv:1507.02287] [INSPIRE]. · DOI
  97. L. Susskind, Black Holes at Exp-time, arXiv:2006.01280 [INSPIRE]. · arXiv
  98. D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE]. · arXiv
  99. J. de Boer, D. Liska, B. Post and M. Sasieta, A principle of maximum ignorance for semiclassical gravity, JHEP 02 (2024) 003 [arXiv:2311.08132] [INSPIRE]. · DOI
  100. A. Climent et al., Universal construction of black hole microstates, Phys. Rev. D 109 (2024) 086024 [arXiv:2401.08775] [INSPIRE]. · DOI
  101. B.S. DeWitt, Quantum Theory of Gravity. 1. The Canonical Theory, Phys. Rev. 160 (1967) 1113 [INSPIRE]. · DOI · Paper page
  102. D.N. Page and W.K. Wootters, Evolution without evolution: dynamics described by stationary observables, Phys. Rev. D 27 (1983) 2885 [INSPIRE]. · DOI
  103. P.A. Hoehn, A.R.H. Smith and M.P.E. Lock, Trinity of relational quantum dynamics, Phys. Rev. D 104 (2021) 066001 [arXiv:1912.00033] [INSPIRE]. · DOI
  104. E. Shaghoulian, The central dogma and cosmological horizons, JHEP 01 (2022) 132 [arXiv:2110.13210] [INSPIRE]. · DOI
  105. E. Shaghoulian, Quantum gravity and the measurement problem in quantum mechanics, arXiv:2305.10635 [INSPIRE]. · arXiv
  106. E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE]. · DOI · Paper page
  107. J. Frohlich and C. King, The Chern-Simons Theory and Knot Polynomials, Commun. Math. Phys. 126 (1989) 167 [INSPIRE]. · DOI
  108. V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982) 515. · DOI
  109. H. Murayama, Explicit Quantization of the Chern-Simons Action, Z. Phys. C 48 (1990) 79 [INSPIRE]. · DOI
  110. A.Y. Alekseev and A.Z. Malkin, Symplectic geometry of the Chern-Simons theory, Lect. Notes Phys. 436 (1994) 59 [INSPIRE]. · DOI
  111. S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory, Nucl. Phys. B 326 (1989) 108 [INSPIRE]. · DOI · Paper page
  112. J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE]. · DOI · Paper page
  113. A.B. Zamolodchikov, Expectation value of composite field $$T\overline{T }$$ in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE]. · arXiv
  114. F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE]. · DOI · Paper page
  115. A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, $$T\overline{T }$$-deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE]. · DOI
  116. V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and $$T\overline{T }$$, JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE]. · DOI
  117. V. Ivo, Y.-Z. Li and J. Maldacena, The no boundary density matrix, JHEP 02 (2025) 124 [arXiv:2409.14218] [INSPIRE]. · DOI
  118. A. Goel, L.V. Iliesiu, J. Kruthoff and Z. Yang, Classifying boundary conditions in JT gravity: from energy-branes to α-branes, JHEP 04 (2021) 069 [arXiv:2010.12592] [INSPIRE]. · DOI

Cited by

Sorted by citations

See all 30

Metadata

Authors
Abdalla, A. I., Antonini, S., Iliesiu, L. V., & Levine, A.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2025-05-07
Volume
2025
Issue
5
ISSN
1029-8479
DOI
10.1007/jhep05(2025)059
Cited by
30
References
13
Language
en
Licence

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review