Pauli-Fierz mass term in modified Plebanski gravity
Résumé
We study SO(4) BF theory plus a general quadratic potential, which describes a bi-metric theory of gravity. We identify the profile of the potential leading to a Pauli-Fierz mass term for the massive graviton, thereby avoiding the linearized ghost. We include the Immirzi parameter in our analysis, and find that the mass of the second graviton depends on it. We discuss the non-perturbative removal of the ghost mode in the light of recent literature. Finally, we discuss alternative reality conditions for the case of SO(3,1) BF theory, relevant for Lorentzian signature, and give a new solution to the compatibility equation.