Determine whether the superpotential defines a known geometric flow

Determine whether the gradient flow generated by the real superpotential on the space of local G2 structures and fluxes is a previously studied geometric flow or a genuinely new flux-dependent flow.

Background

The variational formulation suggests using gradient flow to construct supersymmetric backgrounds numerically. However, convergence is not guaranteed because critical points may be saddles and gauge directions and flux constraints must be handled. Identifying the resulting flow would clarify whether existing analytical and numerical flow techniques apply.

References

Regardless, it would be worth understanding whether the resulting flow is a previously studied geometric flow on the space of $\Gx2$ structures, or a genuinely new one fixed by the flux terms in $\mathcal{W}$.

— A real superpotential for M-theory on eight-manifolds  (2610.12439 - Ashmore et al., 8 Oct 2026) in Section 6, Discussion

Finally, it remains to understand how this story changes for compactifications preserving $N=2$ supersymmetry in three dimensions.

— A real superpotential for M-theory on eight-manifolds  (2610.12439 - Ashmore et al., 8 Oct 2026) in Section 6, Discussion