Determine whether the axion-flux-independent entropy generalizes to higher dimensions

Determine whether the axion-flux-independent on-shell action and entropy found for the dominant three-dimensional axion de Sitter necklace generalize to higher-dimensional axion wormholes.

Background

For the dominant three-dimensional axion necklace selected by the Lorentzian lapse contour, the authors obtain an on-shell action and entropy that are independent of the axion flux q and equal to the empty de Sitter entropy. This result is surprising because the underlying wormhole geometry is sourced by nonzero axion flux.

The paper indicates that it is not established whether this q-independence persists in higher dimensions. Establishing or disproving such a generalization would clarify whether the result reflects a broader universality or is special to three-dimensional axion gravity.

References

We leave a further investigation of this fact, including whether this generalizes to higher dimensions, to future work.

— The cosmological necklace problem  (2609.29859 - Blommaert et al., 24 Sep 2026) in Section 1, immediately following equation (univ)

It would be interesting to understand if a version of this argument generalized to higher dimensions. Is there any contour in the complex $a$ plane for which the on-shell action (see section \ref{sect3:5daxion}) exactly matches the $q=0$ GH action, which deforms to a late-time dS contour? Converse, suppose we take a late-time dS contour and contour deform ``as much as possible'' to the purely Euclidean contour, what wormhole geometry does this produce? We leave this for future investigations.

— The cosmological necklace problem  (2609.29859 - Blommaert et al., 24 Sep 2026) in Concluding remarks, final paragraph of Section 5