Cyclic dg Lie Presentation of the Resolved Theory

Determine whether the ternary operation in the finite cyclic L3 presentation of the resolved heterotic G2 deformation theory can be removed by a further finite stabilization compatible with the cyclic structure.

Background

The paper constructs a finite cyclic L3 model for the resolved heterotic G2 variational theory. Its ternary operation is nonzero in the presented model, as demonstrated by the flat-background constant-mode example, although the existence of a different cyclic presentation is not ruled out.

The unresolved algebraic question is whether a further finite stabilization can eliminate the ternary operation while preserving cyclicity, thereby producing a cyclic differential graded Lie presentation.

References

The present construction gives a finite cyclic L_3 model, but it remains open whether the ternary operation can be removed by a further finite stabilization compatible with the cyclic structure.

— Cyclic $L_3$ Models and Holomorphic Reduction in Heterotic $G_2$ Deformation Theory  (2610.03301 - Brongers, 2 Oct 2026) in Section Consequences and open problems