EFFECTIVE ACTION IN MULTI-DIMENSIONAL SUPERGRAVITIES AND INDUCED EINSTEIN GRAVITY

Abstract

In the present paper a general expression of quantum effective action for arbitrary d-dimensional supergravity on the background Rn×Td−n′ where Rn is n-dimensional curved space-time, Td is d-dimensional torus, is obtained as an expansion on the curvature and its derivatives. The mechanism of inducing Einstein gravity with zero Λ term is proposed. It is shown that the 4-dimensional gravity with the true sign of the Newton constant is induced from d=5 supergravity when antiperiodic boundary conditions are chosen for all fields of supermultiplet. The one-loop effective action is obtained for d=4, 5, 7, 10 supergravities with the accuracy of linear curvature terms. The one-loop Vilcovisky-De Witt effective action is also obtained for d=5 SG’s with the accuracy of linear curvature terms.