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We suggest to consider conformal factor dynamics as applying to compositeboundstates, in frames of the $1/N$ expansion. In this way, a new model ofeffective theory for quantum gravity is obtained. The renormalization group(RG) analysis of this model provides a framework to solve the cosmologicalconstant problem, since the value of this constant turns out to be suppressed,as a result of the RG contributions. The effective potential for the conformalfactor is found too.Comment: 9 pages, LaTeX file, 6-8-1

CONFORMAL FACTOR DYNAMICS IN THE 1/N EXPANSION