We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex poles. According to the literature on Lee-Wick quantization, in this case the theory can be formulated as unitary, since all massive ghosts-like degrees of freedom are unstable.Comment: LaTeX, 15 pages, no figures. Modified version with small misprints corrected and Acknowledgments section inserted. To be published in Physics Letters

Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4-ϵ$ renormalization group for this theory, an approach which proved fruitful in $2-ϵ$ models. A consistent formulation in dimension $n=4-ϵ$ requires taking quantum effects of the topological term into account, hence we perform a calculation which is more general than the ones done before. In the special $n=4$ case we confirm a known result by Fradkin, Tseytlin, Avramidi, and Barvinsky, while contributions from a topological term do cancel. In the more general case of $4-ϵ$ renormalization group equations there is an extensive ambiguity related to gauge-fixing dependence. As a result, physical interpretation of these equations is not universal unless we treat $ϵ$ as a small parameter. In the sector of essential couplings one can find a number of new fixed points, but some of them have no analogs in the $n=4$ case.

In the recently proposed non-local theory of quantum gravity one can avoid massive tensor ghosts at the tree level by introducing an exponential form factor between the two Ricci tensors. We show that at the quantum level this theory has an infinite amount of massive unphysical states, mostly corresponding to complex poles

Conformal gravity is one of the most important models of quantum gravity with higher derivatives. We investigate the role of the Gauss-Bonnet term in this theory. The coincidence limit of the second coefficient of the Schwinger-DeWitt expansion is evaluated in an arbitrary dimension n. In the limit $n=4\mathrm{}$ the Gauss-Bonnet term is topological and its contribution cancels. This cancellation provides an efficient test for the correctness of calculation and, simultaneously, clarifies the long-standing general problem concerning the role of the topological term in quantum gravity. For $n\ne 4$ the Gauss-Bonnet term becomes dynamical in the classical theory and relevant at the quantum level. In particular, the renormalization group equations in dimension $n=4\mathrm{}-\epsilon$ manifest new fixed points due to quantum effects of this term.

The most simple superrenormalizable model of quantum gravity is based on the general local covariant six-derivative action. In addition to graviton such a theory has massive scalar and tensor modes. It was shown recently that in the case when the massive poles emerge in complex conjugate pairs, the theory has also unitary $S$-matrix and hence can be seen as a candidate to be a consistent quantum gravity theory. In the present work we construct the modified Newton potential and explore the gravitational light bending in a general six-derivative theory, including the most interesting case of complex massive poles. In the case of the light deflection the results are obtained within classical and semiclassical approaches.