4 D Quantum N-Dilaton Gravity and One-Loop Divergence of Effective Action on Constant Dilaton

We consider 4D quantum gravity with N-dilatons with the most general couplings. Especially, on constant dilaton and arbitrary metric background, we show the structure of the divergent terms. We show the constraint between the couplings necessary to cancel the coefficient of the square of the Wyle tensor. Next we show the N dependence of a non-renormalizable divergent term, and found that it cannot be canceled in the case of $N \geq 1$ with any fine-tuning of the couplings.