On massive gravitons in 2+1 dimensions

TL;DR

This paper reviews two covariant, parity-preserving massive gravity theories in 3D, demonstrating their linearized equivalence to Fierz-Pauli theory and comparing their features.

Contribution

It clarifies the linearized equivalence of new massive gravity and bigravity in 3D to Fierz-Pauli theory and discusses their similarities and differences.

Findings

Both theories are linearly equivalent to FP theory in 3D.

They are parity-preserving and covariant.

The paper compares their structural differences.

Abstract

The Fierz-Pauli (FP) free field theory for massive spin 2 particles can be extended, in a spacetime of (1+2) dimensions (3D), to a generally covariant parity-preserving interacting field theory, in at least two ways. One is "new massive gravity" (NMG), with an action that involves curvature-squared terms. Another is 3D "bigravity", which involves non-linear couplings of the FP tensor field to 3D Einstein-Hilbert gravity. We review the proof of the linearized equivalence of both "massive 3D gravity" theories to FP theory, and we comment on their similarities and differences.