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

Abstract

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. We show, as an application, that curved versions of these sequences give geometric characterizations of the obstructions to propagation of higher spins in Einstein spaces. Further, we show that projective BGG detour complexes generate both gauge invariances and gauge invariant constraint systems for partially massless models: the input for this machinery is a projectively invariant gauge operator corresponding to the first operator of a certain BGG sequence. We also connect this technology to the log-radial reduction method and extend the latter to Einstein backgrounds.

30 pages, LaTeX

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Cited by in corpus (10)

• Partially Massless Higher-Spin Theory
• Manifest Duality for Partially Massless Higher Spins
• Partially Massless Graviton on Beyond Einstein Spacetimes
• Looking for partially-massless gravity
• Massless and Massive Higher Spins from Anti-de Sitter Space Waveguide
• Kaluza-Klein Reduction of Massive and Partially Massless Spin-2 Fields
• Dynamical Projective Curvature in Gravitation
• Dark Energy From Dynamical Projective Connections
• General structure of Thomas$-$Whitehead gravity
• BGG complexes in singular infinitesimal character for type A