Super-renormalizable quantum gravity

In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers from the unitarity problem because of the presence of a ghost (state of negative norm) in the theory. In this paper, we reconsider the theory first introduced by Tomboulis in 1997, but we expand and extensively study it at both the classical and quantum level. This theory is ghost-free, since the introduction of (in general) two entire functions in the model with the property does not introduce new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to…