A fifth-time action approach to the conformal instability problem in euclidean quantum gravity

Abstract

The fifth-time action technique (a general method for defining bottomless action theories) is applied to euclidean quantum gravity, whose Einstein-Hilbert action is unbounded from below. A stabilized, diffeomorphism invariant action is generated, which has the same classical equations of motion as the unstable euclidean Einstein-Hilbert action. The stabilized action flips the sign of the “wrong-sign” mode in the kinetic term, and is non-local in the interaction terms. Equivalently, Green functions of the stabilized D = 4 theory can be computed from a D = 5 dimensional functional integral, whose “fifth-time” action is local, as well as diffeomorphism invariant and bounded from below. It is argued that the D = 4 Green functions defined in this way are also reflection positive. The D = 5 formulation thus appears to be a good starting point for latticization and numerical simulation.