Bimetric Theory and Partial Masslessness with Lanczos-Lovelock Terms in Arbitrary Dimensions
S. F. Hassan, Angnis Schmidt-May, Mikael von Strauss
TL;DR
The work analyzes ghost-free bimetric theory as a nonlinear arena for partial masslessness (PM) across arbitrary dimensions. By examining proportional backgrounds and the PM Higuchi bound, it shows that two-derivative PM theories exist only in $d=3$ and $d=4$, but Lanczos-Lovelock (LL) terms enable higher-derivative PM theories in dimensions $d>4$, yielding PM candidates in $d=5,6,8$ while ruling out $d=7$. The authors construct nonlinear extensions of the massless and massive sectors and derive polynomial conditions for PM, including explicit parameter relations in several dimensions; they also express the quadratic action and discuss the background-independence of PM data. Overall, the paper extends PM prospects beyond four dimensions by incorporating LL terms and provides concrete PM candidates up to $d=8$, linking to cubic-vertex results and offering a framework for nonlinear PM in ghost-free bimetric theories. The results have implications for the structure of higher-spin interactions in curved backgrounds and the viability of nonlinear PM as a symmetry in gravity-like theories.
Abstract
Ghost-free bimetric theories describe nonlinear interactions of massive and massless spin-2 fields and, hence, provide a natural framework for investigating the phenomenon of partial masslessness for massive spin-2 fields at the nonlinear level. In this paper we analyze the spectrum of the ghost-free bimetric theory in arbitrary dimensions. Using a recently proposed construction, we identify the candidate nonlinear partially massless (PM) theories. It is shown that, in a 2-derivative setup, nonlinear PM theories can exist only in 3 and 4 dimensions. But on adding Lanczos-Lovelock terms to the bimetric action it is found that higher derivative nonlinear PM theories also exist in higher dimensions. This is consistent with existing results on the direct construction of cubic vertices with PM gauge symmetry. We obtain the candidate nonlinear PM theories in 5, 6 and 8 dimensions but show that none exist in 7 dimensions.