Massive Gravity Theories and limits of Ghost-free Bigravity models

TL;DR

This work shows that ghost-free bigravity built from Lovelock invariants admits scaling limits that reproduce New Massive Gravity (NMG) and generate a broad class of higher-curvature, BD-ghost-free theories in arbitrary dimensions. A central construction is a determinant-type interaction that, under suitable parameter choices, reduces to Born-Infeld gravity in 3D and generalizes to new BD-ghost-free determinant actions in higher dimensions, including connections to DBI gravity and holographic c-theorems. The authors also prove BD ghost absence for the Lovelock bigravity class via a careful decoupling limit and antisymmetric polynomial structure, while showing that Schouten-tensor extensions generally reintroduce the ghost. The results illuminate deep ties between massive gravity, Galileon dynamics, and holographic duals, offering a unified path to ghost-free, higher-curvature gravity theories with potential CFT duals.

Abstract

We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic $c$-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic $c$-theorems.