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

TL;DR

This paper develops a non-linear, ghost-free theory of interacting spin-2 fields with a partially massless symmetry based on an SO(1,5) extension, advancing understanding of higher-spin gravity models.

Contribution

It introduces a novel SO(1,5)-based non-linear theory of spin-2 fields with partial masslessness, maintaining symmetry to all orders and avoiding ghost instabilities.

Findings

Constructed a ghost-free, non-linear spin-2 theory with PM symmetry.

Demonstrated the SO(2) symmetry becomes PM transformations perturbatively.

Identified the role of a vector field in enabling order-by-order symmetry construction.

Abstract

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. In this context, the vector field is crucial to circumvent earlier obstructions to an order-by-order construction of PM symmetry. Although the non-linear theory lacks enough first class constraints to remove all helicity-0 modes from the spectrum, the PM transformations survive to all orders. The absence of ghosts and strong coupling effects at the non-linear level are not addressed here.