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Covariant Monolayer and Bilayer Holographic Entropy Proposals (de Sitter)

Develop and validate a covariant holographic entanglement entropy prescription for de Sitter static patch holography by proving either the monolayer formula S_mono(A)=min_ext[Area(γ_E)/(4G)]+O(G^0) or the bilayer formula S_bil(A)=min_ext[Σ_I Area(γ_I)/(4G)]+O(G^0), where the extremal surfaces γ_I are D_I-homologous to A across the interior and exterior regions bounded by the screens.

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Background

In static patch holography, the holographic screen sits in the bulk, raising the question of how to compute dual entanglement entropy. The monolayer proposal uses only the exterior region; the bilayer sums over interior and exterior contributions. The thesis formulates both covariantly and argues the bilayer is consistent while the monolayer has issues.

References

Conjecture [Covariant monolayer and bilayer proposals] Let $A$ be a subsystem of $\Sigma\vert_{\mathcal{S}{\rm L}\cup\Sigma\vert{\mathcal{S}{\rm R}$. According to the monolayer proposal, the entanglement entropy of $A$ is given by \begin{equation} \label{eq:mono} S{\rm mono}(A)= \min \mathrm{ext}\left[\frac{\rm Area}(\gamma_E)}{4G}\right] +O(G0). \end{equation} According to the bilayer proposal, \begin{equation} \label{eq:bil} S_{\rm bil}(A)= \min \mathrm{ext}\left[\sum_{I=L,E,R}\frac{\rm Area}(\gamma_I)}{4G}\right] +O(G0), \end{equation} where $\gamma_I$ must be $D_I$-homologous to $A$.

— Information-theoretic constraints in quantum gravity and cosmology (2510.15787 - Franken, 17 Oct 2025) in Chapter: Bridging the static patches: Connectivity of de Sitter space, Section: Covariant monolayer and bilayer proposals