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

TL;DR

This paper investigates the existence of nonlinear partially massless theories within ghost-free bimetric models across various dimensions, revealing that higher derivative terms enable their existence beyond four dimensions.

Contribution

It demonstrates that Lanczos-Lovelock terms allow for nonlinear partially massless theories in higher dimensions, extending previous results limited to 3 and 4 dimensions.

Findings

Nonlinear PM theories exist only in 3 and 4 dimensions without higher derivatives.

Adding Lanczos-Lovelock terms enables nonlinear PM theories in 5, 6, and 8 dimensions.

No nonlinear PM theories are found in 7 dimensions with these methods.

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.