Spin-locality without one-form vertex symmetries

Determine whether spin-locality can be achieved for holomorphic zero-form vertices that do not satisfy the corresponding one-form-sector symmetries.

Background

The paper establishes that specific dualities and additional assumptions on holomorphic one-form-sector vertices are sufficient, and in a meaningful sense necessary, for constructing spin-local zero-form vertices of the constrained form satisfying the vanishing condition at y=0.

It remains unresolved whether the same locality property might hold for vertices outside this constrained class, namely vertices lacking the associated one-form symmetries.

References

Whether spin-locality can also be achieved for vertices not of this form, i.e. without the corresponding one-form symmetries, remains an open question.

— Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector  (2609.24956 - Valerev, 21 Sep 2026) in Section 1, Introduction, subsection “General background”