Abstract
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.
Highlights
One of the main guidelines in extending this theory was to demand the existence of a holographic c-function [9, 10], in order to constrain the possible form of the higher curvature terms in the action
We show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is free of the Boulware-Deser ghost
This culminated in the proposal of a completely nonlinear theory of massive gravity in four dimensions [4] which is guaranteed to be free of the Boulware-Deser ghost in a known decoupling limit [3] and has since been proven ghost-free nonlinearly [15, 16] following the arguments of [4]
Summary
We will be interested in a class of ghost-free d-dimensional bigravity models which are natural generalizations of the models introduced in [5] utilizing the d-dimensional generalization of the finite number of allowed mass-terms given in [4]. As shown in [4], when fab is the Minkowski metric Kba is the unique tensor that picks out the Galilean invariant combination of the helicity zero mode Kba ∝ ∂a∂bπ in the appropriate decoupling limit Ma, Mb → ∞ keeping m2Ma fixed This gives a simple explanation for why the mass term must be a characteristic polynomial in Kab since only these combinations of ∂a∂bπ are total derivatives, a necessary requirement to ensure that the equations of motion for π are second order. It explains the connection between decoupling limits of massive gravity models and Galileon models since the helicity-zero mode always enters in this Galileon invariant combination. A generalization of the proof of the absence of a BD ghost for these Lovelock bigravity models is given in appendix C
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