# Looking for partially-massless gravity

## TL;DR

This paper investigates the theoretical possibilities for constructing a consistent, unitary partially-massless spin-two field theory interacting with gravity across dimensions, revealing connections to conformal gravity and novel non-geometric couplings.

## Contribution

It demonstrates that gauge-invariant interactions of partially-massless spin-two fields necessitate massive fields and relate to conformal gravity, proposing new unitary theories under relaxed symmetry conditions.

## Key findings

- Interaction invariants lead to conformal gravity structures.
- Unitary theories possible in 4D with parity violation.
- Non-geometric couplings offer alternative unitary models.

## Abstract

We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that the gauge and parity invariant interaction of PM spin two particles requires the inclusion of specific massive spin-two fields and leads to a reconstruction of Conformal Gravity, or multiple copies of the latter in even dimensions. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but this theory cannot be constructed in the standard formulation, due to the absence of the parity-odd cubic vertex therein. Finally, by relaxing the general covariance, we show that a `non-geometric' coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory. We also clarify some aspects of interactions between massless, partially-massless and massive fields, and resolve disagreements in the literature.