Massive Higher Spins from BRST and Tractors

TL;DR

This paper derives higher spin equations of motion using a BRST approach within tractor calculus, unifying massive, massless, and partially massless spins in conformally flat backgrounds and enhancing holographic correspondence understanding.

Contribution

It introduces a tractor-based, BRST derivation of higher spin equations that unifies different mass regimes and clarifies conformal invariance in higher spin theories.

Findings

Derived higher spin tractor equations of motion from BRST methods.

Proved these equations describe various spin states in conformally flat backgrounds.

Enhanced understanding of bulk-boundary conformal geometry in holography.

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 system manifest. In this approach, physical systems are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive systems 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.