Asymptotic Freedom in Renormalisable Gravity and Supergravity

Abstract

Pure Einstein gravity is known to be non-renormalizable. Though the theory is one-loop finite on shell it probably possesses a divergent S-matrix starting from the two-loop order. The situation is even worse when ordinary matter is added. Quantizing matter fields in the classical metric background we already need bare curvature squared R²-terms in order to absorb the infinities. The possible was of improvement suggest themselves: (i) we may try to arrange all matter fields in a multiplet in order to cancel dangerous divergences. This is the way of supergravity known to be only partially successful at present (only one- and two-loop on shell finiteness was established); (ii) one can add the R²-terms to the Einstein langragian thus obtaining a manifestly renormalizable theory.