Role of higher-point cluster coordinates in strong- and finite-coupling descriptions

Determine whether the cluster coordinates obtained from periodic momentum-twistor constructions play a direct role in the strong-coupling minimal-surface and $Y$-system description or in the finite-coupling form-factor operator-product expansion.

Background

The paper develops cluster coordinates for weak-coupling form-factor symbol alphabets using periodic momentum twistors. It then notes that periodic form-factor geometry also appears in strong-coupling minimal surfaces and associated YY-systems, while finite-coupling collinear dynamics is organized by the form-factor OPE.

The unresolved issue is whether the cluster coordinates constructed in the weak-coupling algebraic framework have a direct interpretation or utility in either of these nonperturbative or finite-coupling descriptions.

References

It remains to understand whether the cluster coordinates found here have a direct role in either description.

— Form Factor Alphabets and Antipodal Duality from Cluster Algebras  (2609.04839 - He et al., 4 Sep 2026) in Section 5, “Summary and outlook”