Classification of half‑maximal consistent truncations

Classify all consistent truncations of ten- and eleven-dimensional supergravity that preserve half-maximal supersymmetry with compact gauge groups, providing a complete characterisation analogous to the known maximal-supersymmetry result where sphere and group-manifold reductions exhaust all possibilities.

Background

The paper highlights that for maximally supersymmetric truncations with compact gauge groups, a complete classification is known: consistent truncations are precisely those on spheres and group manifolds. This serves as a benchmark for what a full classification can look like.

By contrast, for the half-maximal case, despite new families of consistent truncations constructed here using torsion-free Spin(n) structures in Spin(n,n) generalised geometry, there is no analogous comprehensive classification. Establishing such a catalogue would systematise when and how half-maximal truncations arise, including intrinsically generalised-geometry examples where flux and generalised structures are essential.