  A perturbative quantum theory of the two Killing vector reduction of Einstein
gravity is constructed. Although the reduced theory inherits from the full one
the lack of standard perturbative renormalizability, we show that strict cutoff
independence can be regained to all loop orders in a space of Lagrangians
differing only by a field dependent conformal factor. A closed formula is
obtained for the beta functional governing the flow of this conformal factor.
The flow possesses a unique fixed point at which the trace anomaly is shown to
vanish. The approach to the fixed point is compatible with Weinberg's
``asymptotic safety'' scenario.
