Resolution of interior Q_i-H pinch singularities

Determine whether a finite-distance interior degeneration in which one quadratic factor Q_i and the master function H simultaneously vanish can admit an intrinsically M-theoretic resolution, such as a regular bolt, orbifold limit, brane throat, or additional conserved-charge interpretation, within or beyond the cohomogeneity-one GMMW ansatz.

Background

Under the paper’s finite-limit hypotheses, an isolated interior zero of one Q_i forces a double zero with H=H'=0 and requires the other two curvature coefficients to be positive. The resulting metric has divergent curvature at finite proper distance, with one base factor decompactifying while complementary directions collapse.

The authors find no numerical example of such a pinch and do not establish whether it can be resolved by an intrinsically M-theoretic mechanism. They explicitly distinguish this unresolved issue from the proved classification of possible first losses of regularity.

References

We therefore interpret a $Q_i$--$H$ pinch as a boundary at which the classical compactification breaks down. Within the present ansatz, we find no indication that it is a removable bolt, an orbifold limit, a regular brane throat, or a source carrying an additional independent conserved charge. We find that these conditions are necessary only. No such pinch is realized numerically here, and whether such a boundary admits an intrinsically M-theoretic resolution is a separate question we do not touch.

— Beyond the polynomial ansatz: regular $AdS_3\times M_8$ solutions of M-theory  (2610.20853 - Gregory, 14 Oct 2026) in Section 6.2, “Finite degeneration mechanisms”