Bimetric Theory and Partial Masslessness with Lanczos-Lovelock Terms in Arbitrary Dimensions

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.