$O(d,d;\mathbb{Z})$ invariant Fierz-Pauli massive gravity

TL;DR

This paper develops an $O(d,d; Z)$ invariant massive gravity theory within double field theory, deriving consistent conditions and identifying new classes of ghost-free, tachyon-free models with specific parameter sets.

Contribution

It introduces a novel $O(d,d; Z)$ invariant massive deformation of double field theory and characterizes the conditions for ghost and tachyon absence, leading to new massive gravity models.

Findings

Derived diagonalized second order actions for each helicity mode.

Established consistency conditions including the weak constraint.

Identified two-parameter families of ghost-free, tachyon-free massive gravity theories.

Abstract

We consider an $O(d,d;\mathbb{Z})$ invariant massive deformation of double field theory at the level of free theory. We study Kaluza-Klein reduction on $R^{1,n-1} \times T^{d}$ and derive the diagonalized second order action for each helicity mode. Imposing the absence of ghosts and tachyons, we obtain a class of consistency conditions which include the well known weak constraint in double field theory as a special case. Consequently, we find two-parameter sets of $O(d,d;\mathbb{Z})$ invariant Fierz-Pauli massive gravity theories.