A 4-DIMENSIONAL THEORY FOR QUANTUM-GRAVITY WITH CONFORMAL AND NONCONFORMAL EXPLICIT SOLUTIONS

The most general version of a renormalizable d = 4 theory correspondin g to a dimensionless higher-derivative scalar field model in curved sp acetime is explored. The classical action of the theory contains 12 in dependent functions, which are the generalized coupling constants of t he theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power typ e is proven to consist of precisely three conformal and three non-conf ormal solutions, given by remarkably simple (albeit non-trivial) funct ions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. Th e stability of the finite solutions is investigated and the possibilit y of renormalization-group flows is discussed as well as possible phys ical applications.