Unitarity of Weyl-invariant new massive gravity and generation of graviton mass via symmetry breaking

Abstract

We give a detailed analysis of the particle spectrum and the perturbative unitarity of the recently introduced Weyl-invariant version of the new massive gravity in $2+1$ dimensions. By computing the action up to second order in the fluctuations of the metric, the gauge and the scalar fields around the anti-de Sitter (AdS) and flat vacua, we find that the theory describes unitary (tachyon and ghost-free) massive spin-2, massive (or massless) spin-1 and massless spin-0 excitations for certain ranges of the dimensionless parameters. The theory is not unitary in de Sitter space. Scale invariance is either broken spontaneously (in AdS background) or radiatively (in flat background) and hence the masses of the particles are generated either spontaneously or at the second loop order.