Partial Masslessness and Conformal Gravity

TL;DR

This paper investigates the properties of partially massless spin 2 fields within conformal gravity, revealing limitations in extending their interactions beyond linear order due to higher-spin consistency issues.

Contribution

It demonstrates the constraints on extending partially massless fields in conformal gravity, highlighting propagation only in Einstein backgrounds and the nature of interaction vertices.

Findings

Partially massless fields propagate only in Einstein backgrounds.

Conformal gravity generates only cubic order interaction vertices.

Higher-order extensions face known higher-spin consistency obstructions.

Abstract

We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conformal gravity's Bach tensor into Einstein times Schouten operators. We find that extending PM beyond linear order suffers from familiar higher-spin consistency obstructions: it propagates only in Einstein backgrounds, and the conformal gravity route generates only the usual safe, Noether, cubic order vertices.