Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity

Understand

We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders.

• This theory is based on the SO(1,5) group, in analogy with the SO(2,4) formulation of conformal gravity, but has a quadratic spectrum free of ghost instabilities.
• The action contains a vector field associated to a local SO(2) symmetry which is manifest in the vielbein formulation of the theory.
• We show that, in a perturbative expansion, the SO(2) symmetry transmutes into the PM transformations of a massive spin-2 field.