Guilherme de Berredo-Peixoto and Ilya L. Shapiro

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. For the conformal case the $n \to 4$ limit agrees with the previous calculation by Antoniadis-Mottola and in part with the one by Fradkin-Tseytlin. In the general non-conformal case we confirm a known result by Fradkin-Tseytlin and Avramidi-Barvinsky, while contributions from the 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.

Facultad de Ciencias, Seminario de Tercer Ciclo de F&i&sica Aplicada. Universidad de Zaragoza