Pinning down M-theory's free parameters with hidden symmetries

One of string and M-theory's persistent problems is that compactifications generically leave a continuous family of free parameters—moduli—with no dynamical reason to prefer one value over another. By tracking which duality symmetries survive when M-theory is compactified on tori with a non-trivial spin structure, the authors locate discrete fixed points in moduli space that are pinned by symmetry and therefore isolated. Explicit constructions are worked out for compactifications to eight, six, five, and four spacetime dimensions. A proposed anomaly-cancellation condition for orbifold variants generalizes the level-matching rule familiar from perturbative string theory to a fully duality-covariant setting.