Interpretation of the two saddles as Wilsonian renormalization-group flows

Determine whether the Riemannian and non-Riemannian bulk saddles represent distinct Wilsonian renormalization-group flows from the same supersymmetric fixed point.

Background

The paper constructs Riemannian and everywhere non-Riemannian bulk completions of the same Gomis–Ooguri boundary geometry. Both are presented as candidate radial trajectories emanating from a common supersymmetric fixed point, but their interpretation in terms of Wilsonian renormalization-group evolution is not established.

Resolving this issue would clarify whether the two bulk branches represent genuinely distinct effective descriptions of the boundary theory or merely alternative saddle configurations within a single holographic setup.

References

Their interpretation as distinct Wilsonian RG flows remains open.

— Non-Riemannian Holography: Long Strings and Soft Hair  (2610.25669 - Hampton et al., 19 Oct 2026) in Conclusion

The Euclidean continuation, the assignment of temperature and entropy, the choice of a common ensemble, and the relative weights of the saddles in~RGKPW remain open questions.

— Non-Riemannian Holography: Long Strings and Soft Hair  (2610.25669 - Hampton et al., 19 Oct 2026) in Supplemental Material, Section SM 1.2, “Non-Riemannian Saddle Action”