Partial masslessness and conformal gravity
Journal of Physics A: Mathematical and Theoretical
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
... structions: it propagates only in Einstein backgrounds, and the conformal gravity route generates only the usual safe, Noether, cubic order vertices. PACS : 04.62.+v, 04.50.-h, 04.50.Kd, 04.62.+v, 02.40.-k 1 Recall that there are three varieties of spin 2 excitations in dS: massive, massless and partially massless [1, 2] The latter enjoy an interesting mixed behavior: In dS they propagate lightlike, positive energy (inside the maximally accessible intrinsic dS horizon), helicity ±2, ±1 excitations in a unitary representation of the dS isometry group [3, 5, 4, 6] . This degree of freedom (DoF) count relies on the gauge invariance (1) and a divergence constraint ∇ µ ϕ µν = ∇ ν ϕ, where ϕ := ϕ ρ ρ .