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

The most general version of a renormalizable d = 4 theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains 12 independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three non-conformal solutions, given by remarkably simple (albeit non-trivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization-group flows is discussed as well as possible physical applications.