Metric projective geometry, BGG detour complexes and partially massless gauge theories

Understand

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems.

• Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry.
• We show that the BGG machinery of projective geometry combines with structures known as Yang-Mills detour complexes to produce a general tool for generating invariant pseudo-Riemannian gauge theories.
• This produces (detour) complexes of differential operators corresponding to gauge invariances and dynamics.