Massive Gravity in Three Dimensions

A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model, which also includes “topologically-massive” gravity as a special case, propagates the two spin-2 helicity states with different masses. We discuss the extension to massive $\mathcal{N}$-extended supergravity, and we present a “cosmological” extension that admits an anti–de Sitter vacuum.