Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-12-17
Physics
High Energy Physics
High Energy Physics - Theory
25 pages. v2: modified sections 1, 2 and 4 to improve presentation
Scientific paper
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. At the non-perturbative level, we find a situation similar to genuine bi-gravities: even choosing the Pauli-Fierz mass term, the ghost mode propagates through the interactions. We present some simple potentials leading to two and three degrees of freedom, and discuss the difficulties of finding a ghost-free bi-gravity with seven degrees of freedom. 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.
Beke David
Palmisano Giovanni
Speziale Simone
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