Quantum gravity in an AdS space-time is described by an SU(N) Yang-Mills theory on a sphere, a bounded many-body system. We argue that in the high temperature phase the theory is intrinsically non-perturbative in the large N limit. At any nonzero value of the \\\'t Hooft coupling $lambda$, an exponentially large (in N^2) number of free theory states of wide energy range (of order N) mix under the interaction. As a result the planar perturbation...