Higher Derivative Quantum Gravity with Gauss-Bonnet Term

Abstract

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