Asymptotic freedom in gauge theories and quantum gravity

Restrictions on the structure of a gauge theory which follow from the requirement of asymptotic freedom with respect to all coupling constants are studied. One-loop counterterms for renormalizable gravity with matter are computed. It is shown that for the group O(N), taking into account the contribution of quantum R²-gravity allows one to construct new, asymptotically free gauge theories with a reduced number of spinor multiplets. The results are compared with those obtained earlier for conformal gravity with matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–41, January, 1990.The authors thank A. O. Barvinskii, I. L. Bukhbinder, and E. S. Fradkin for the discussions.