Gauge and global symmetries of the candidate partially massless bimetric gravity

TL;DR

This paper examines the symmetry properties of a specific ghost-free bimetric gravity theory, revealing that its partially massless symmetry is limited to cubic order and cannot be extended further, impacting the understanding of such theories.

Contribution

It demonstrates that the partially massless symmetry in the considered bimetric theory cannot be extended beyond cubic order, clarifying limitations of symmetry extensions in these models.

Findings

Global SO(1,4) symmetry enhances to SO(1,5) at quadratic order

Partially massless symmetry is inconsistent at cubic order

Symmetry cannot be extended beyond cubic order in these theories

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.