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.

• Received 22 December 2004

DOI:https://doi.org/10.1103/PhysRevD.71.064005