Gauge and global symmetries of the candidate partially massless bimetric gravity

TL;DR

The paper examines a ghost-free bimetric theory that exhibits partially massless (PM) symmetry at quadratic order, where the global symmetry appears enhanced to $SO(1,5)$ but is shown to be inconsistent beyond cubic order. By expanding the action to cubic and quartic orders, the authors derive non-linear PM transformations and analyze the closure of global symmetries, finding that the $SO(1,5)$ algebra is accidental and does not survive non-linear interactions. They demonstrate an obstruction to extending PM gauge symmetry beyond cubic order, and show that no quartic or higher-order PM-invariant action exists for a theory with one massless and one massive spin-2 field. The results align with no-go theorems for non-linear PM gravity and suggest that achieving PM symmetry non-linearly requires enlarging the field content or exploring alternative frameworks. These findings illuminate the constraints on constructing fully consistent non-linear PM theories within two-spin-2 field setups and inform directions for future work in higher-spin and multi-field extensions.

Abstract

In this paper we investigate a particular ghost-free bimetric theory that exhibits the partially massless (PM) symmetry at quadratic order. At this order the global SO(1,4) symmetry of the theory is enhanced to SO(1,5). We show that this global symmetry becomes inconsistent at cubic order, in agreement with a previous calculation. Furthermore, we find that the PM symmetry of this theory cannot be extended beyond cubic order in the PM field. More importantly, it is shown that the PM symmetry cannot be extended to quartic order in any theory with one massless and one massive spin-2 fields.