Massive higher spins from BRST and tractors

Abstract

We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit systems manifest. In this approach, physical models are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive models can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk–boundary correspondence.