Looking for partially-massless gravity

TL;DR

The paper analyzes whether a unitary partially-massless spin-2 field can consistently couple to gravity across dimensions. It shows that gauge and parity invariance typically require extra massive spin-2 content and lead, in even dimensions, to Conformal Gravity or its multiples, while strict covariance and a finite field content yield a no-go via an admissibility constraint. By relaxing parity or general covariance, new, potentially unitary avenues emerge (e.g., parity-violating PM gravity in D=4 or non-geometric couplings), though these paths involve non-standard formulations and additional degrees of freedom that demand further investigation. The work also clarifies how massless, PM, and massive spin-2 interactions must organize under global symmetries and resolves several discrepancies in the literature. Overall, the results delineate the boundaries of unitary PM gravity within conventional frameworks and point to alternative, non-standard formulations as possible but challenging routes forward.

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.