Virtual or enumerative invariants for heterotic G2 moduli

Determine whether moduli spaces of heterotic G2 systems admit virtual or enumerative invariants, and characterize the role of the additional compatibility data identified by the derived comparison in constructing such invariants.

Background

The effective potential captures the ordinary formal deformation space over Artin algebras concentrated in degree zero, whereas the compatibility-resolved theory retains additional derived information detected over dg-Artin algebras. The discussion proposes that a global derived description could provide an appropriate framework for studying virtual or enumerative invariants of heterotic G2 moduli. The role of the additional compatibility data in such a theory is explicitly left unresolved.

References

Such a global derived description would also provide a natural setting in which to ask whether heterotic $G_2$ moduli admit virtual or enumerative invariants: the present comparison identifies additional compatibility data whose role in a virtual or enumerative theory remains to be determined.

— Derived deformation theory of heterotic $G_2$ systems near the standard embedding  (2609.35071 - Brongers, 28 Sep 2026) in Section 7, Discussion