Determine a finite-dimensional central-charge extremization principle

Determine whether restricting the real superpotential to a finite-dimensional family of trial geometric data fixes the central charge of the dual two-dimensional N=(1,0) SCFT without solving the full supersymmetry conditions, and identify the geometric data that plays the role of the Reeb vector.

Background

For N=(0,2) AdS3 backgrounds, c-extremization has a geometric counterpart involving a finite-dimensional family of trial data and a Reeb vector. Minimal N=(1,0) supersymmetry lacks a trial R-symmetry, so the paper asks whether the real superpotential can nevertheless provide a comparable finite-dimensional extremization principle.

References

A more modest question remains, however: whether restricting $\mathcal{W}$ to a finite-dimensional family of trial data fixes $c$ without needing the full supersymmetry conditions. In particular, one would want to know what geometric data on $X$ plays the role that the Reeb vector plays in GK geometry.

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