In a de Sitter space, there are three spin-2 representations of the SO(1,5) isometry group: massless, massive, or partially massless. By analogy with SO(2,4) conformal gravity, here a SO(1,5) theory of interacting partially massless spin-2 fields is constructed in the vielbein formulation. It has a ghost-free quadratic spectrum, and a local SO(2) vector gauge field which generates the partially massless transformations of the spin-2 field. There are also dynamical helicity-zero modes.

Earlier attempts to construct a partially massless spin-2 theory order-by-order met with difficulties - but here, one begins with an SO(1,3) x SO(2) gauge theory, and the presence of the SO(2) vector field is what ultimately gives you correct partially massless transformations. It remains an open question whether this theory contains ghosts/strong coupling at the non-linear level.