de Sitter and Cosmological-Horizon Holography

De Sitter space has a horizon entropy and temperature, asymptotic conformal structure, and observer-dependent static patches, but no agreed analogue of the standard AdS boundary construction. At the 2026-08-20 evidence cutoff, wave-function proposals and static-patch operator algebras capture important semiclassical structures. A complete positive, operational, nonperturbative, and unique microscopic dual is not known. Global, observer, and compactification questions must be assessed separately.

Helpful background. de Sitter and Cosmological-Horizon Holography develops global and static-patch coordinates, horizon thermality, and principal holographic proposals.

One geometry, several holographic questions

Global de Sitter has spacelike past and future boundaries, while a timelike observer accesses only one static patch. A late-time wave function, a Euclidean boundary correlator, a thermal trace, and an observer algebra are different objects. Agreement on the de Sitter temperature $T=1/(2\pi L)$ is not enough to identify them because the geometry already fixes that number.

Assessment at 2026-08-20	Meaning
Question status	Open
Evidence status	Insufficient evidence for a complete unique dual; supported for several semiclassical structures
Confidence	High
Domain	Global or static patch, declared state/inner product, observer, contour, dimension, and microscopic construction
What could change the conclusion	Validation of the shock-wave adverse test or a complete positive microscopic model

A candidate dual should say what its states are, how conjugation and positivity work, which observables one observer can measure, and whether it computes a wave function or a trace. Entropy matching without these structures is diagnostic but not a definition.

A starting project: understand the static-patch trace

This is an advanced analytic direction. Before choosing it, be able to explain KMS states, modular flow, gravitational constraints, and the difference between a finite trace and a finite-dimensional Hilbert space. Start with the linked de Sitter background, then read Chandrasekaran, Longo, Penington, and Witten 2023, §2.4, Eqs. (28)–(31). Extract the observer-energy restriction, state, algebra, and normalization of the trace. Consult the earlier construction whenever an operator in those equations has not been defined.

Reconstruct the normalization and cyclicity argument for the proposed trace and explain where the de Sitter KMS property enters. Follow the role of the observer variable instead of replacing it with an arbitrary finite matrix. Check how the maximum-entropy state is represented and why a type-II algebra is not the algebra of matrices on a finite number of states. A finite-matrix analogue can illustrate entropy normalization, but cannot establish the claimed algebra type.

Deliver an annotated derivation with the assumptions attached to each step and a comparison of algebraic versus thermodynamic entropy conventions. This needs access to the papers and mathematical supervision more than computing power. If modular theory is unfamiliar, make the KMS and trace derivation the reading objective before committing to a de Sitter duality project.

A possible research extension is to test one precisely specified perturbation of the state or observer prescription while retaining a controlled algebra and gravitational approximation. Check subsequent positive and adverse results, including those below, before deciding that this is open. Pivot if a necessary positivity or cyclicity step cannot be justified. Neither geometric horizon entropy nor a successful semiclassical trace calculation by itself supplies a unique microscopic de Sitter dual.

The global wave-function proposal

Strominger identified Euclidean conformal structures in asymptotic de Sitter symmetries and free-field wave functions Strominger 2001, §§5–8. This motivates dS/CFT-like descriptions in which late-time wave-function coefficients resemble Euclidean CFT correlators. Complex conformal weights, the choice of inner product, and observer accessibility obstruct a direct reading as an ordinary unitary Lorentzian boundary theory.

Witten emphasizes the structural differences from AdS: there is no globally timelike positive-energy generator, and asymptotic quantities at spacelike infinity do not coincide with the measurements available to one causal observer Witten 2001, pp. 1–15. Analytic continuation can generate formulas but does not automatically supply a physical Hilbert space or positive probabilities.

Results and open questions at 2026-08-20

Evidence	Secure structure	Required interpretation	Unresolved issue
Asymptotic dS/CFT proposal	Euclidean conformal behavior of symmetries and wave functions	Global late-time data	Inner product, positivity, and observer access
Foundational adverse analysis	No global positive-energy time and unusual observables	Quantum gravity in global de Sitter	Complete operational formulation
Static-patch type-II$_1$ algebra	Observer-inclusive semiclassical algebra and entropy relation	Constrained static patch with an observer	Unique finite microscopic theory
Positive-energy de Sitter shock/time-advance test	Challenges cyclicity/positivity of a specified trace proposal	The tested Euclidean static-patch construction	Applicability to other observer algebras
Compactification control analysis	Lists scale, localization, and correction requirements	Candidate classical de Sitter backgrounds	Fully controlled stable microscopic realization

Observer algebras and generalized entropy

Chandrasekaran, Longo, Penington, and Witten include an observer and impose semiclassical constraints to obtain a type-II$_1$ static-patch algebra with a trace and generalized-entropy relation Chandrasekaran et al. 2023, §§2–4. This is a controlled algebraic advance: it makes observer dependence precise and avoids demanding naive local tensor factors.

An infinite-dimensional von Neumann factor is not by itself a finite microscopic Hilbert space with dimension $e^{S_{\mathrm{dS}}}$. Nor does an algebraic trace uniquely determine the ultraviolet theory. The construction should be judged as a semiclassical organization of observables unless and until a microscopic model realizes it.

Positive-energy shocks and the negative-shock terminology

Chen, Stanford, Tang, and Yang study positive-energy shock waves on a de Sitter horizon Chen et al. 2026, §1 and §§2.2–3.1. Their homogeneous profile produces a time advance rather than the familiar black-hole time delay, and the corresponding regularized eikonal OTOC increases. The paper’s “negative shocks” terminology concerns the opposite sign of the de Sitter shock profile and the negative shock modes entering the continuation and resummation; it does not mean negative-energy matter sources the physical shock.

The resulting conflict with cyclicity or positivity is a strong recent preprint-level adverse test, but its conclusion must remain proposal specific. The calculation tests a proposed equality between observer-worldline correlators computed by a Euclidean static-patch path integral and a Hilbert-space trace under stated analyticity assumptions. It does not refute every observer algebra or global wave-function description. Independent verification should reproduce the shock profile, eikonal continuation, operator ordering, state preparation, and positivity assumption before the result is generalized.

Microscopic and string-theory control

A positive lower-dimensional critical point is not yet a controlled de Sitter vacuum. One must check flux quantization, tadpoles, source localization, all compactification radii, weak string coupling, $\alpha'$ and loop corrections, the full mass spectrum, scale separation, and decay channels. Andriot and Ruehle analyze these requirements for candidate classical solutions Andriot and Ruehle 2024, §§2.3–4.3.

These physical requirements are logically independent of the algebraic ones. A beautiful static-patch algebra need not identify a string vacuum, while a metastable critical point need not provide the observer’s exact quantum algebra.

Adverse evidence and failed routes

The central unresolved gap is the absence of a model satisfying all four demands at once: microscopic definition, positive state space, operational observer algebra, and controlled de Sitter geometry. This is a literature gap, not a null search with stated sensitivity. Matching entropy or temperature alone is underdetermined. Analytically continuing an AdS answer without specifying conjugation and contour is another failed shortcut.

The shock-wave calculation is an adverse test of one claimed trace structure under its assumptions, not a universal no-go. Likewise, lack of parametric control in a compactification ansatz does not prove that de Sitter quantum gravity is impossible; it removes that ansatz from the controlled-evidence set.

What would change the assessment

A complete microscopic construction would need a positive Hilbert-space or algebraic formulation, explicit observer observables, correct KMS and real-time correlators, generalized entropy, and a controlled gravitational limit. A string realization would additionally require quantized data, scale hierarchy, stabilization, and calculable lifetime.

The status would also change after independent validation or refutation of the 2026 shock-wave result, because it targets a concrete positivity property. Any repair must show exactly which trace, contour, or operator domain changes.

Research checklist

• Distinguish global wave-function data from static-patch observables and thermal traces.
• Define states, conjugation, inner product, and positivity before calling an object a dual.
• Identify the observer and the algebra operationally available to it.
• Check KMS periodicity, cyclicity, reflection positivity, and real-time continuation.
• State whether the algebra is semiclassical or a unique microscopic theory.
• For compactifications, verify fluxes, tadpoles, radii, coupling, corrections, masses, and decay.
• Do not infer a complete dual from the geometric entropy or temperature alone.

Source and data map

Strominger supplies the asymptotic proposal; Witten supplies the foundational obstructions; the 2023 work supplies the observer algebra; the 2026 shock-wave preprint supplies the strongest current adverse test; and the compactification analysis supplies the microscopic-control checklist. No correlator or compactification search was rerun for this assessment. Reproduction requires KMS, cyclicity, positivity, backreaction, flux quantization, all scales, corrections, localization, mass spectra, and decay.

References

• Andriot, D., and F. Ruehle. “On Classical de Sitter Solutions and Parametric Control.” arXiv:2403.07065v2 (2024). arXiv.
• Chandrasekaran, V., R. Longo, G. Penington, and E. Witten. “An Algebra of Observables for de Sitter Space.” Journal of High Energy Physics 02 (2023) 082. doi:10.1007/JHEP02(2023)082.
• Chen, Y., D. Stanford, H. Tang, and Z. Yang. “Negative Shocks versus Static Patch Holography.” arXiv:2607.14042v1 (2026). arXiv.
• Strominger, A. “The dS/CFT Correspondence.” Journal of High Energy Physics 10 (2001) 034. doi:10.1088/1126-6708/2001/10/034.
• Witten, E. “Quantum Gravity in de Sitter Space.” arXiv:hep-th/0106109 (2001). arXiv.