ON THE CONFORMAL-TRANSFORMATION AND DUALITY IN GRAVITY

The theory described by the sum of the Einstein-Hilbert action and the action of a conformal scalar field possesses the duality symmetry, wh ich includes some special conformal transformation of the metric, and also inversion of the scalar field and of the gravitational constant. In the present paper the conformal duality is generalized for an arbit rary spacetime dimension n not equal 2 and for the general sigma-model type conformal scalar theory. We also consider applying the conformal duality to the investigation of quantum gravity in the strong curvatu re regime. The trace of the first coefficient of the Schwinger-DeWitt expansion is derived and its dependence on the gauge fixing condition is considered. Finally, we discuss the way to extract the gauge-fixing independent result and also its possible physical applications.