The dS/dS Correspondence

Andreas Karch; David Tong; Eva Silverstein; Mohsen Alishahiha

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The dS/dS Correspondence

Mohsen Alishahiha, Andreas Karch, Eva Silverstein, David Tong

High Energy Physics - Theory · Submitted 14 Jul 2004 · 48 references

Pith's verdict: A well-motivated, honestly-hedged proposal for static-patch dS holography whose one real gap — the UV matching at the central slice — the authors name themselves.

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arXiv IDhep-th/0407125 (version 2)

Pith IDA7HPMEAC, Pith's permanent record of this paper and its review

CitationAndreas Karch, David Tong, Eva Silverstein, Mohsen Alishahiha. "The dS/dS Correspondence." arXiv:hep-th/0407125 (2004). https://pith.science/paper/A7HPMEAC

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Editor's note

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The thing to know: this is the paper that recasts the dS static patch as two cut-off CFTs on dS_{d-1}, glued at the central slice and coupled to (d-1)-dimensional gravity. That statement is new relative to Strominger's dS/CFT and to the RS multi-throat holography it borrows its template from, and it rests on something concrete rather than analogy alone: the dS_d and AdS_d metrics in dS_{d-1} slicing agree at leading order near the horizon (Eq. 2.2), so the near-horizon DBI actions agree, and the entropy counting against Gibbons-Hawking (S = R^{d-2} M_d^{d-2}) and the induced Newton constant (2.4)-(2.5) both land where they should. The §3 analysis of D3 probes in Schwarzschild-AdS5 stands on its own — reading the DBI expansion as a thermal average of multitrace couplings, and giving a field-theory account of why probes take forever to reach a horizon, is real work that does not depend on the dS proposal being right. The diffusion constant D = R in d = 5 is a clean check too, even if the section around it is thin. On the stress-test note: half right, half restatement. Yes, the metric coincidence is only O(ρ²/R²) and fails at ρ ~ R. But the paper never claims otherwise — the isomorphism is an IR statement by construction, and the central slice is precisely where the two throats differ and get matched. So 'the analogy fails at the cutoff' is the acknowledged §2.4 gap, not a separate mechanism. The sharper version is narrower: the Pöschl-Teller bound states (2.8) are the only UV-sensitive data the paper computes, the authors say they encode how the throats are cut off and coupled, and then they do not decode them. That is where I would press. Other soft spots, in proportion: §2.4 is candid that the matching is undetermined, so the abstract's flat 'We present a holographic duality' runs slightly ahead of the body; the hydrodynamics section asserts more than it derives (D = R in d = 5, a log divergence in d = 4, an infinite answer in radial slicing); the claim that the two CFTs are in causal contact rather than entangled is stated without argument; the M2 appendix assumes the ⟨Tr(∂η)⁴⟩ scaling rather than computing it, though it says so. Who should read it: anyone working on dS holography or on holographic renormalization of Newton's constant in warped throats. It earns referee time as a proposal, not as a derivation. Send it out, and cite it.

Referee report

Significance

If correct, the proposal gives a self-contained dual description of a single observer's causal patch, with the bulk entropy carried by field-theory degrees of freedom rather than by the (d-1)-dimensional graviton, and it connects de Sitter holography to the well-understood holography of two-throated Randall-Sundrum and warped compactifications. The brane-probe analysis also offers a field-theoretic reading of the fact that probes take forever to reach a horizon in general relativity, as strong back reaction on a rolling scalar near points with light states. The paper is honest about its incompleteness, and the consistency checks it does offer are individually sound. There are no free parameters or invented entities; the entropy benchmark S = R^{d-2} M_d^{d-2} is the external Gibbons-Hawking result, and the KK mass gap is computed from the analogue Schroedinger problem.

Major objections (4)

[Abstract and S2.4] The abstract (sentence s1) states flatly that dS_d(R) 'is holographically dual to two conformal field theories on dS_{d-1}(R)', whereas S2.4 states 'our statement of holographic duality is not complete' because the matching of the full theory to the CFT at the scale 1/R has not been determined. This is a mismatch in the status being claimed, and it is fixable: the abstract and the S1 summary should be tempered to present the duality as a proposal whose cutoff matching is left open, in the same way that 'Randall-Sundrum is just CFT coupled to gravity' is a useful but incomplete statement. As written, a reader who stops at the abstract will take away a stronger claim than the body supports.
[S2, Eq. (2.2)] The identification of the near-horizon dS_d region with a CFT on dS_{d-1} rests on the leading-order coincidence of the dS_d and AdS_d metrics in dS_{d-1} slicing, which the authors correctly describe as holding only 'at leading order in a low energy expansion, that is neglecting the corrections of order rho^2/R^2 = E^2/T^2' (S2). The duality is then defined by cutting the CFTs off at E ~ 1/R, exactly where rho^2/R^2 = O(1) and the two geometries are not isomorphic. The consistency checks offered -- the KK mass gap (2.7), the induced Newton constant (2.4)-(2.5), and the diffusion constant D=R in d=5 -- are all IR probes (E << 1/R) and therefore do not test the central-slice boundary condition. The authors acknowledge the gap in S2.4, so this is not a new finding, but the paper should state explicitly which of its checks probe the cutoff and which do not, so that the reader can see that the defining ingredient is asserted by analogy in a regime where the analogy's premise is known to fail at O(1).
[S2.2, Eq. (2.8)] The Poeschl-Teller bound states are described as encoding 'details about the way the two throats are cut off and coupled to each other', and the authors say 'It would be interesting to decode their effects in detail.' These bound states are the one place in the KK analysis where UV-sensitive data enters, and they are left undecoded. Decoding at least the first extra mode (which the text says appears in d=5) would give the proposal a concrete, checkable statement at the cutoff and would be the most direct way to address the gap noted in the previous comment. As it stands, the only UV handle the paper identifies is not used.
[S3.1, Eq. (3.5) and S3.2] The interpretation of the DBI square-root factor as a thermal average of a multitrace operator is presented as a guess ('arises from the thermal average of a term of the form'), and the authors state 'we have little hope of determining it from first principles.' The subsequent matching in Eq. (3.9) is at a supersymmetry-protected order, and the claim that the probe action 'contains information about the entropy' rests on the partial S/partial N counting, which is itself inferred rather than derived. This is acceptable as an interpretation, but since S4 builds on it, the paper should distinguish explicitly which statements in S3-S4 are derived and which are conjectural, rather than presenting the thermal-average reading as established.

Minor objections (6)

[Eq. (2.6)] The potential term as printed contains a stray factor in the 1/cosh^2(z/R) coefficient; please check the coefficient, since the bound-state spectrum (2.8) depends on it.
[Eq. (2.8) and S2.2] The text states that the first extra bound state in d=5 'translates into a mode of negative mu^2', but Eq. (2.8) gives the KK mass m_l^2, which for d=5 and l=1 is positive. The relation between m_l^2 and the dS_{d-1} frequency mu^2 invoked in S2.2 should be stated, so that the sign statement is transparent.
[S2.3, Eq. (2.9)] The statement that D=R in d=5 is 'consistent with the thermal interpretation' would benefit from one sentence on what independent expectation it is being compared to, since the computation itself is the check.
[S4.4] The iteration to higher codimension, culminating in a quantum-mechanical description independent of any gravitational sector, is deferred to reference [11] ('work in progress'). This is acceptable, but the programmatic nature of the claim should be flagged in the text rather than stated as an expected outcome.
[S4.3] The connection between the timescale restriction stated in the abstract and the domain-wall/vacuum-bubble analysis of S4.3 could be made more explicit, so that the reader sees how the decay of the de Sitter phase is mirrored in the dual.
[Figures 1 and 2] The captions refer to the behavior of g_{00} at the horizon and at the central slice; a short annotation of the E=0 and E=1/R endpoints directly on the figures would make the UV/IR correspondence easier to read.

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The paper

The paper claims

The static patch of de Sitter space is proposed to be dual to two cutoff conformal field theories on a de Sitter slice, coupled to each other and to lower-dimensional gravity.

The reading

The paper proposes a holographic dual for the region of de Sitter space that a single observer can actually see — the static patch — rather than for the whole global spacetime. The claim is that $d$-dimensional de Sitter space with curvature radius $R$ is equivalent to two conformal field theories living on $(d-1)$-dimensional de Sitter space of the same radius, each cut off at energy $1/R$, coupled to each other and to dynamical $(d-1)$-dimensional gravity at the join. The argument runs through the de Sitter slicing of (A)dS: near the horizon the geometry is indistinguishable from the corresponding AdS slice, so the low-energy physics is ordinary cutoff CFT, while the central slice where the warp factor peaks is where the two theories meet and where a normalizable graviton zero mode gives the lower-dimensional Newton constant. If correct, this gives a self-contained description of one observer's causal region in which the bulk of the entropy is carried by field-theoretic degrees of freedom, and it explains why probes never reach a horizon as a statement about strong backreaction in the dual field theory rather than as a quirk of general relativity.

What carries the argument

The load-bearing object is the de Sitter slicing of (A)dS, $ds^2=e^{2A(w)}$ times the $dS_{d-1}$ metric plus $dw^2$, with $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$. In the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$.

Extended reading notes

Core claim

The central claim is that the $dS_d(R)$ static patch is holographically dual to two conformal field theories on $dS_{d-1}(R)$, cut off at energy scale $1/R$, where they couple to each other and to $(d-1)$-dimensional gravity. The supporting structure is a parallel treatment of $dS_d$ and $AdS_d$ foliated by $dS_{d-1}$ slices, with warp factors $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$; in the paper's coordinates the warp factors are $e^{2A(w)}=R^{-2}$ times $R^2$ factors given by $e^{2A(w)}=R^{-2}$ times $R^2$ factors of $1$.

Load-bearing premise

The paper assumes that the joining of the two cutoff field theories at the central slice, including all the couplings and boundary conditions there, can be treated as two conformal field theories coupled to each other and to lower-dimensional gravity; the authors state in §2.4 that they have not determined this matching, so the duality is stated as a template rather than a complete definition.

Editorial extensions

If this is right

A single observer's causal patch in de Sitter has a self-contained quantum description that does not require the full global spacetime or an entanglement interpretation across horizons.
The $(d-1)$-dimensional Newton constant computed by dimensional reduction, $1/G_{N,d-1}\sim S\,(1/R)^{d-3}$ with $S$ the horizon entropy in Planck units, agrees with the renormalization expected from $S$ field-theoretic modes cut off at $1/R$.
The graviton Kaluza-Klein spectrum on the sliced background has a normalizable zero mode plus a continuum above the gap $m^2>(d-2)^2/(4R^2)$, matching the spectrum expected for conformal field theory on de Sitter space.
The fact that a probe takes forever to reach a horizon in general relativity becomes a field-theory statement: the rolling scalar suffers strong backreaction from higher-derivative couplings to the thermalized degrees of freedom, giving an approach law such as $\varphi-\varphi_0\sim c\,e^{-4\varphi_0 t/\sqrt{\lambda}}$.
Vacuum bubbles and domain-wall shells in the bulk correspond to domain walls and vacuum transitions in the dual field theory, so nonperturbative decay of de Sitter can be described on the field-theory side.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the matching at the central slice can be fixed, the same construction should give a controlled count of states for any observer: the finite cutoff means a finite-dimensional Hilbert space, which is exactly the kind of bookkeeping that a de Sitter entropy bound demands.
The proposal suggests a concrete comparison target for numerical or lattice studies of strongly coupled theories on curved backgrounds: the diffusion constant extracted from the horizon, $D=R$ in $d=5$, is a sharp number the dual field theory should reproduce.
Iterating the reduction to higher codimension points toward a purely quantum-mechanical description of the static patch, which would let one ask whether the entropy is carried by field-theoretic degrees of freedom all the way down.
The parallel with two-throat Randall-Sundrum geometries implies that existing warped-compactification technology — matching conditions, radion dynamics, Kaluza-Klein decomposition — can be imported directly into de Sitter holography.

Original abstract

We present a holographic duality for the de Sitter static patch which consolidates basic features of its geometry and the behavior of gravity and brane probes, valid on timescales short compared to the decay or Poincare recurrence times. Namely de Sitter spacetime $dS_d(R)$ in $d$ dimensions with curvature radius $R$ is holographically dual to two conformal field theories on $dS_{d-1}(R)$, cut off at an energy scale 1/R where they couple to each other and to $d-1$ dimensional gravity. As part of our analysis, we study brane probes in de Sitter and thermal Anti de Sitter spaces, and interpret the terms in the corresponding DBI action via strongly coupled thermal field theory. This provides a dual field theoretic interpretation of the fact that probes take forever to reach a horizon in general relativity.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,804 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We present a holographic duality for the de Sitter static patch which consolidates basic features of its geometry and the behavior of gravity and brane probes, valid on timescales short compared to the decay or Poincare recurrence times. Namely de Sitter spacetime $dS_d(R)$ in $d$ dimensions with curvature radius $R$ is holographically dual to two conformal field theories on $dS_{d-1}(R)$, cut off at an energy scale 1/R where they couple to each other and to $d-1$ dimensional gravity. As part of our analysis, we study brane probes in de Sitter and thermal Anti de Sitter spaces, and interpret the terms in the corresponding DBI action via strongly coupled thermal field theory. This provides a dual field theoretic interpretation of the fact that probes take forever to reach a horizon in general relativity.

background contribution method result interpretation main claim

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	We present a holographic duality for the de Sitter static patch which consolidates basic features of its geometry and the behavior of gravity and brane probes, valid on timescales short compared to the decay or Poincare recurrence times.	contribution 0.96	0.91	0.71	asserted 1.00
s1	Namely de Sitter spacetime $dS_d(R)$ in $d$ dimensions with curvature radius $R$ is holographically dual to two conformal field theories on $dS_{d-1}(R)$, cut off at an energy scale 1/R where they couple to each other and to $d-1$ dimensional gravity.	result 0.68	0.76	0.77	asserted 1.00
s2	As part of our analysis, we study brane probes in de Sitter and thermal Anti de Sitter spaces, and interpret the terms in the corresponding DBI action via strongly coupled thermal field theory.	contribution 0.77	0.92	0.06	asserted 0.98
s3	This provides a dual field theoretic interpretation of the fact that probes take forever to reach a horizon in general relativity.	interpretation 1.00	0.57	0.10	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.63.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** A spatial slice of the static patch of dSd, with the dSd−1 slices and the behavior of the redshift factor g00 shown. The bulk of the d dimensional spacetime is described by conformal field theories on dSd−1 at energy scales E ranging from 0 to of order 1/R, where they are cut off and coupled to each other and to d − 1 dimensional gravity, which is localized at the central slice where g00 = 1. We have indicated dSd−1 slices near the IR end on each side, on which we can consider brane probes realizing the approximate Coulomb branch of the low energy CFTs. This leads to the following…

**Figure 2.** The two-throated Randall-Sundrum or warped compactification depicted here has a similar holographic duality: the dual is given by a pair of field theories cut off in the UV and coupled to each other and to d − 1 dimensional gravity. In the bulk of this paper, we will analyze the D-brane and gravity probes of these geometries, and the related case of dS-sliced AdS (which is isomorphic to our case at low energies). The gravity probe analysis yields a localized graviton (as well as a finite set of 3

**Figure 3.** A domain wall shell in the static patch. Note that the bubble wall intersects the dSd−1 slices on which the field theory lives also as a vacuum bubble in the field theory. As in the thermal field theory case discussed in §3, this probe takes forever to fall into the dSd horizon at rs = R in the general relativity approximation. Again this follows from a combination of summed higher derivative and thermal effects in the probe DBI action SDBI = −τB Z r 2 s d 2Ωdt√ h p 1 − r˙ 2 s /h2 (4.7) where τB is the tension of the brane probe. Now let us consider the interpretation of the

Figures reproduced from arXiv:hep-th/0407125 by the authors.

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How the literature uses it

103 arXiv papers cite this in 160 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 · 96 sentences without a confident label

Compares with it 3 papers

This matches the dS/dS formulation of the analogous entanglement entropy in [ref] .[In that framework, the UV slice playing the role of the boundary of each of the two sectors in [ref] automatically lies at the maximal surface, with no room between them to move it off-center in tracing out one of the two systems.] As just mentioned, we address the issue of off-shell contributions which naively provide stronger contributions to the path integral by incorporating UV effects, in the simplest, $U(1)$-symmetric, setting where the question arises.

The yes boundaries wavefunctions of the universe · Summary of main results and organization of the paper · 0.96
We note that this foliation of the static patch is similar to the one that inspires the “$dS/dS$” correspondence [ref] .

Bra-ket wormholes in gravitationally prepared states · The $π$ contour · 0.92
In particular, we discuss the relationship of our description of de Sitter spacetime with the DS/dS correspondence [ref] and the Shaghoulian-Susskind proposal [ref] .

Black Hole and de Sitter Microstructures from a Semiclassical Perspective · Intrinsically two-sided systems · 0.91

Cites it as background 55 papers

Let us set up the notation for the basic DS/dS framework [ref] .

Entropy, Entanglement and Swampland Bounds in DS/dS · Setup and notation · 0.93
In addition, other holographic duality models in the dS spacetime, such as the dS/dS holography [ref] and half-dS holography [ref] , have also gained attention and been studied.

Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS$_3$/CFT$_2$ · Introduction · 0.97
However, we are still lacking understandings of holography in de Sitter space (dS), so-called dS/CFT correspondence [ref] (see also [ref] ), though there has been a concrete proposal in four-dimensional higher spin gravity [ref] , and interesting recent progresses in the light of the dS/dS correspondence [ref] , holographic entanglement entropy [ref] , and holography in dS static patch [ref] .

Holography in de Sitter Space via Chern-Simons Gauge Theory · Introduction · 0.99

Discussion

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