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Derivation of the Correct de Sitter Holographic Entropy Prescription

Derive, from a bulk path-integral computation, the correct holographic entanglement entropy prescription in static patch holography in order to decide between competing formulations and remove ambiguities about extremization versus constrained extremization.

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Background

The thesis presents both restricted maximin/extremal and constrained-extremal prescriptions, showing inequivalences and arguing for a constrained extremization scheme to maintain consistency. However, it notes that only a path-integral derivation (analogous to HRT in AdS) can conclusively select the correct prescription.

References

We do not prove which is the correct prescription. To answer this question, one should derive it from a path integral computation.

— 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 holographic entanglement entropy