Extension of holomorphic one-form vertices to the full nonlinear system

Determine whether the all-order holomorphic one-form-sector vertices computed in the holomorphic generating system are restrictions of vertices of the full nonlinear unfolded higher-spin system, including the mixed sector.

Background

The construction relies on cyclicity and prefactor conditions satisfied by known lower-order vertices and by the all-order holomorphic one-form-sector vertices obtained in the work cited as Povarnin.

The relationship between those holomorphic vertices and the vertices of the complete nonlinear unfolded higher-spin equations, which include mixed holomorphic–antiholomorphic contributions, has not been established.

References

Nevertheless, whether the vertices from are restrictions to the holomorphic sector of the full nonlinear unfolded higher-spin vertices (including the mixed sector) remains an open question.

— Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector  (2609.24956 - Valerev, 21 Sep 2026) in Section 2, subsection “Requirements for the one-form sector vertices”

Hence, it remains an open question how exactly to choose $B_n$ in the even-$n$ case, and we leave this subtlety for future investigation.

— Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector  (2609.24956 - Valerev, 21 Sep 2026) in Section 6, Conclusion