Determine the origin of the additional Hartle–Hawking contribution

Determine whether the additional Hartle–Hawking contribution absent from the single-thimble de Sitter minisuperspace and Liouville-zero-mode calculations is carried by nonzero Liouville modes or by integration cycles of the full theory.

Background

The paper finds a single de Sitter Lefschetz thimble in the matched bulk minisuperspace and boundary Liouville-zero-mode truncations, consistent with analyses based on a positive Lorentzian lapse. The authors contrast this result with settings in which a Hartle–Hawking-type saddle contributes.

They explain that the discrepancy may result from the truncation to SO(3)-invariant variables or from different nonperturbative contour prescriptions. The paper does not determine whether the missing Hartle–Hawking contribution arises from nonzero Liouville modes or from integration cycles available only in the full theory.

References

It remains possible that the additional Hartle--Hawking contribution is carried by nonzero Liouville modes or by integration cycles of the full theory.

— Stokes Phenomena between AdS/CFT and dS/CFT  (2609.10677 - Honda et al., 9 Sep 2026) in Discussion section, paragraph beginning “This distinction also clarifies the different dS saddle content.”

We see no reason to expect the dominant contribution from small reheating surfaces to be precisely canceled by the remaining contributions to the norm. We leave these issues for future work.

— Logarithmic gravity from a very slow roll limit of inflation  (2609.38052 - Cotler et al., 29 Sep 2026) in Section 2.4, “The no-boundary norm with an inflaton is not zero,” final paragraph before the summary