de Sitter Holography: Dictionary Completeness, Obstructions, and Status

A complete de Sitter holographic dictionary would identify a boundary object, state space or algebra, state, inner product, observables, time evolution, bulk reconstruction, entropy interpretation, and nonperturbative definition in one fixed theory. Existing proposals fill different subsets of this checklist. As of 10 August 2026, none fills it generically, and gaps must not be supplied by AdS analogy.

Required background. de Sitter and Cosmological Holography supplies the proposal classes; de Sitter Observables, States, and Horizon Patches fixes observable domains; dS/CFT Dictionaries and Analytic Continuation fixes the continuation claim.

Helpful background. Static-Patch Algebras and Observer Dependence supplies the observer algebra. For current QFT obstructions use Cosmological Bootstrap: Loops, Initial States, Validity, and Handoffs, Massless Zero Modes and the Invariant-State Obstruction, Interacting Infrared Logs and Secular Regimes, Infrared Resummation and Dynamical Mass, Stochastic Coarse-Graining and Its Derivation from QFT, Langevin and Fokker–Planck Dynamics, Stationary Distributions and First-Passage Observables, QFT–Stochastic Matching and Renormalization, and Quasi-de Sitter Validity and Evidence Status.

Completeness criteria

For a proposal $P$, ask for the tuple

$$P=(\mathcal B,\mathcal H\text{ or }\mathcal A,\rho, \langle\cdot,\cdot\rangle,\mathcal O,t,\mathcal R, S_{\mathrm{dS}},\mathcal Z_{\mathrm{np}}),$$

where $\mathcal B$ is the boundary object, $\mathcal A$ an observer algebra if no Hilbert factorization is available, $\mathcal O$ the observable set, $\mathcal R$ a bulk reconstruction map, and $\mathcal Z_{\mathrm{np}}$ a nonperturbative definition. Each entry needs a regime and falsifier. A late-time coefficient can fill $\mathcal B$ and part of $\mathcal O$ while leaving every other entry open.

First application: a dated proposal matrix

Proposal	Defined object and state	Quantitative support	Missing or obstructed entry	Strongest licensed status
Asymptotic dS/CFT	Future-boundary wavefunction/generating functional; usually Bunch–Davies contour	Free kernels, conformal Ward identities, continued perturbative diagrams	Positive inner product, finite-time observer map, generic reconstruction, nonperturbative fixed theory	Conditional late-time semiclassical dictionary
Static-patch algebra	Worldline-dressed observer algebra with KMS state; type II$_1$ after semiclassical gravitational constraint	Detector thermality, algebraic trace, generalized-entropy differences	Global observables, arbitrary backreaction, microscopic completion, relation to $\mathcal I^+$	Controlled semiclassical observer algebra
Higher-spin dS/$Sp(N)$	Nonunitary Euclidean vector-model partition function as Hartle–Hawking wavefunction	Current spectrum, continued two- and three-point functions, functional determinants	Reflection positivity, static-patch reconstruction, pseudo-local interaction class, finite-$N$ completion	Explicit model of late-time wavefunction data
dS JT/matrix-like models	Specified lower-dimensional amplitudes and genus expansion with contour	Exact moduli integrals and resurgent structure	Unique integration cycle, fixed-theory versus ensemble meaning, higher-dimensional extrapolation	Solvable model-dependent quantum cosmology
Finite-Hilbert-space proposals	Horizon entropy interpreted as $\log\dim\mathcal H$	Semiclassical $A/(4G_N)$; model-dependent overlap counts	Exact state basis, observer map, factorization, QFT limit, stable UV completion	Conjectural microscopic interpretation

The original dS/CFT proposal establishes the conformal and wavefunction target Strominger 2001, §§ 2–4. The static algebra gives a different, observer-relative object Chandrasekaran et al. 2023, §§ 2–5. Higher-spin functional determinants probe nontrivial wavefunction deformations Anninos et al. 2014, §§ 3–5. dS JT supplies an explicit nonperturbative/resurgent laboratory with unusual continuation data Cotler and Jensen 2024, §§ 2–5. These are independent supports for partial dictionaries, not cumulative proof of one shared theory.

Current proposals do not erase missing maps

A June 2025 preprint proposes a microscopic de Sitter entropy count using nonorthogonal thin-shell geometries and wormhole overlaps Wang 2025, §§ 2–5. An August 2026 preprint proposes a Lorentzian-torus realization of dS/CFT and reports entropy, correlator, and pseudoentropy matches Fujiki et al. 2026, §§ 2–5. Both are current primary proposals inside this cutoff. Neither has yet supplied a generally accepted positive inner product, fixed-theory finite-time reconstruction, and ultraviolet-complete four-dimensional model; their affirmative calculations should be recorded without upgrading unsettled entries.

QFT obstructions also remain. Massless zero modes can prevent a de Sitter-invariant Fock state, interacting fields generate infrared or secular logarithms, and stochastic resummation describes a coarse-grained sector rather than a complete holographic boundary theory. Quasi-de Sitter evolution lacks exact de Sitter symmetry. A holographic proposal must state whether it excludes, resums, or reconstructs these regimes.

Regime controls

Every semiclassical row assumes $G_NH^{d-1}\ll1$. A top-down claim must also state $g_s$, $\alpha'H^2$, Kaluza–Klein gaps, moduli stabilization, and vacuum lifetime. Higher-spin dS has no high-spin gap; dS JT has no local graviton; static-algebra results assume a perturbative observer and clock. These limitations are different and cannot be pooled into one generic error bar.

Adversarial control: demand a normalized finite-time answer

Fix one static observer, Bunch–Davies state, finite switching interval, and relational scalar detector. Ask each proposal for the normalized probability distribution and a reconstruction map in one fixed theory. The static algebra and QFT define the semiclassical observable. A late-time partition function must supply the Born-rule inner product and reconstruction; a lower-dimensional model answers only its analogue; an entropy count supplies neither. Mark absent entries as absent.

Then test factorization and contour independence beyond perturbation theory. If changing a matrix contour or wormhole prescription changes the answer while preserving the semiclassical saddle, the completion was not fixed. If a proposal requires complex dimensions, retain the failed reflection-positivity test as a limitation.

The evidence ceiling through the stated date is a set of substantial partial results: late-time coefficient dictionaries, an observer algebra, solvable higher-spin and low-dimensional models, and active entropy proposals. There is no settled complete, unitary, observer-compatible, nonperturbative de Sitter holographic dictionary. New evidence and comparative confidence require a dated research update; the stable textbook conclusion is the explicit pattern of defined and missing structures.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Anninos, D., Denef, F., Konstantinidis, G., and Shaghoulian, E. (2014). “Higher Spin de Sitter Holography from Functional Determinants.” Journal of High Energy Physics 2014(2), 007. DOI.
• Chandrasekaran, V., Longo, R., Penington, G., and Witten, E. (2023). “An Algebra of Observables for de Sitter Space.” Journal of High Energy Physics 2023(2), 082. DOI.
• Cotler, J., and Jensen, K. (2024). “Non-Perturbative de Sitter Jackiw–Teitelboim Gravity.” Journal of High Energy Physics 2024(12), 016. DOI.
• Fujiki, K., Kohara, M., Moreno, J., Shinmyo, K., and Takayanagi, T. (2026). “de Sitter Holography from a Lorentzian Torus.” arXiv:2608.01729 [hep-th]. Preprint.
• Strominger, A. (2001). “The dS/CFT Correspondence.” Journal of High Energy Physics 2001(10), 034. DOI.
• Wang, Z. (2025). “Microscopic Origin of the Entropy of de Sitter Spacetime.” arXiv:2506.03058 [hep-th]. Preprint.