Radiatively stable ghost and tachyon freedom in metric affine gravity
C. De Marzo
Abstract
We report the existence of a ghost- and tachyon-free sector in metric affine theories of gravity, that is invariant under diffeomorphism and a particular Abelian symmetry. In contrast with many studied cases in the literature, the constraints for unitarity and causality are granted by nonaccidental symmetries and do not ask for further tuning, whose fate under renormalization would be unclear. Unsurprisingly, the minimal model is massless. We find that a mechanism to provide mass is accommodated by a simple Stueckelberg extension of metric affine gravity involving the nonmetricity tensor. A nontrivial result is that also such an extension describes a ghost- and tachyon-free dynamic stabilized by the same Abelian symmetry. The resulting spectrum of the collective rank-3, rank-2, and rank-0 Lagrangian is investigated with the operators recently computed in the literature.