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

Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity