Some Aspects of the de Sitter/CFT Correspondence

Dietmar Klemm

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Some Aspects of the de Sitter/CFT Correspondence

Dietmar Klemm

High Energy Physics - Theory · Submitted 26 Jun 2001

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

The authors' main claim Requiring the pressure to be positive yields an upper bound for the black hole mass, given by the mass of the Nariai solution.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.85 · mentions code or data availability 0.01.

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We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories. The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter space is derived both from the conformal anomaly and the transformation law of the CFT stress tensor when going from dS_3 in planar coordinates to dS_3 with cosmological horizon. The two-point correlator for CFT operators coupling to bulk scalars is obtained in static coordinates, corresponding to a CFT on a cylinder. Correlation functions are also computed for CFTs on two-dimensional hyperbolic space. We furthermore determine the energy momentum tensor and the Casimir energy of the conformal field theory dual to the Schwarzschild-de Sitter solution in five dimensions. Requiring the pressure to be positive yields an upper bound for the black hole mass, given by the mass of the Nariai solution. Beyond that bound, which is similar to the one found by Strominger requiring the conformal weights of CFT operators to be real, one encounters naked singularities.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories.	contribution 0.68	0.70	0.09	asserted 0.47
s1	The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter space is derived both from the conformal anomaly and the transformation law of the CFT stress tensor when going from dS_3 in planar coordinates to dS_3 with cosmological horizon.	result 0.80	0.90	0.20	asserted 1.00
s2	The two-point correlator for CFT operators coupling to bulk scalars is obtained in static coordinates, corresponding to a CFT on a cylinder.	result 0.76	0.92	0.05	asserted 1.00
s3	Correlation functions are also computed for CFTs on two-dimensional hyperbolic space.	result 0.67	0.89	0.04	asserted 1.00
s4	We furthermore determine the energy momentum tensor and the Casimir energy of the conformal field theory dual to the Schwarzschild-de Sitter solution in five dimensions.	result 0.66	0.94	0.11	asserted 1.00
s5	Requiring the pressure to be positive yields an upper bound for the black hole mass, given by the mass of the Nariai solution.	result 0.99	0.86	0.18	asserted 1.00
s6	Beyond that bound, which is similar to the one found by Strominger requiring the conformal weights of CFT operators to be real, one encounters naked singularities.	interpretation 0.53	0.55	0.22	asserted 0.99

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Original abstract

We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories. The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter space is derived both from the conformal anomaly and the transformation law of the CFT stress tensor when going from dS_3 in planar coordinates to dS_3 with cosmological horizon. The two-point correlator for CFT operators coupling to bulk scalars is obtained in static coordinates, corresponding to a CFT on a cylinder. Correlation functions are also computed for CFTs on two-dimensional hyperbolic space. We furthermore determine the energy momentum tensor and the Casimir energy of the conformal field theory dual to the Schwarzschild-de Sitter solution in five dimensions. Requiring the pressure to be positive yields an upper bound for the black hole mass, given by the mass of the Nariai solution. Beyond that bound, which is similar to the one found by Strominger requiring the conformal weights of CFT operators to be real, one encounters naked singularities.

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References

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Cited by 16 Pith papers

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Exploring de Sitter Space and Holography
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Stress Tensor Deformations in dS/CFT: Mixed Boundary Conditions, Spectrum Flow and Pseudo Entropy
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Conformal Vacua and Entropy in de Sitter Space
hep-th 2001-12 conditional novelty 7.0 of 10

The choice of de Sitter invariant vacuum changes the dS/CFT boundary correlators, for dS3 by a marginal deformation, and Cardy's formula with c = 3l/2G reproduces the Kerr-dS3 horizon entropy.

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The dS/CFT Correspondence and the Big Smash
hep-th 2001-12 conditional novelty 6.0 of 10

Exact non-singular phantom cosmologies exist that avoid the Big Smash, but a holographic renormalization-group argument may exclude them if the dual CFTs are conventional.
Holography in flipped AdS/$\mathbb{Z}$: Another approach to dS holography
hep-th 2026-08 conditional novelty 5.0 of 10

Quantum field theories in de Sitter space and in a signature-flipped compact-time spacetime (fAdS) are related by analytic continuation, and the proposed fAdS/fCFT holographic dictionary reproduces de Sitter horizon e...
Holographic Complexity in dS$_{d+1}$
hep-th 2022-02 accept novelty 5.0 of 10

All three holographic complexity proposals in de Sitter spacetime diverge as a universal power law at a finite critical time and grow linearly after cutoff regulation.
De Sitter Space and Entanglement
hep-th 2019-01 conditional novelty 5.0 of 10

The Gibbons-Hawking entropy of de Sitter space is derived as the holographic entanglement entropy between its past and future conformal boundaries, and the bulk entanglement between its two Rindler wedges is computed ...
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The paper reviews holographic renormalization and shows that near-boundary AdS results, including the Brown-York stress tensor, continue to de Sitter space up to a dimension-dependent sign.
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How the literature uses it

20 arXiv papers cite this in 36 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

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Compares with it 3 papers

This average is given by [equation] finally obtaining [equation] Thereby, the central charge in the large $q-$limit corresponds [equation] exactly as has been previously derived in the dS$_3$/CFT$_2$ correspondence [ref] .

de Sitter Entanglement and Conformal Description of the Cosmological Horizon · dS$_3$ holography from $4$ dimensions · 0.93
As we shall see, the total central charge of the two boundaries reproduces exactly the central charge derived in the context of the dS$_3$/CFT$_2$ correspondence [ref] .

Liouville description of conical defects in dS$_4$, Gibbons-Hawking entropy as modular entropy, and dS$_3$ holography · Introduction · 0.90
The value of the central charge agrees with [ref] and is imaginary for the dual CFT of dS$_3$, as mentioned above.

Aspects of dS/CFT Holography · Central Charge in dS$_3$ · 0.95

Cites it as background 13 papers

According to the dS/CFT correspondence [ref] , its precursors [ref] and refinements [ref] , the microscopic degrees of freedom giving rise to the dS entropy are encoded within a dual Euclidean conformal field theory located at the boundary of global dS space.

De Sitter Space and Entanglement · The problem of de Sitter entropy · 0.87
In comparison to AdS/CFT's brane-dynamical constructuring [ref] and prosperous developing [ref] , dS/CFT [ref] especially dS/CFTe has never been implemented/invented top-downly and has been only rarely(relative to AdS/CFT) explored in string communities due to the difficulty of de Sitter vaccum's brane-constructuring [ref] .

Emergent time axis from statistic/gravity dualities · Basic ideals on emergent space-time · 0.87
Some papers have proposed the dS/CFT correspondence, which describes that quantum gravity in de Sitter space is dual to CFT living on the past and future boundaries of de Sitter space [ref] , where the masses of the stable scalar make the conformal weights become complex, hence the boundary CFT is non-unitary.

Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model · Introduction · 0.90

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