  The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using
the exact renormalization group equations has been studied, motivated by the
recently found non-trivial fixed point in $4<d<6$ dimensions with metastable
critical potential. Particular attention is paid to the case of $d=5$ where the
scaling exponent $\nu$ has the value $1/3$, which coincides with the scaling
exponent of quantum gravity in one fewer dimensions. Convincing results show
that this relation could be generalized to arbitrary number of dimensions above
five. Some aspects of AdS/CFT correspondence are also discussed.
