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Quantum gravity in an AdS spacetime 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 λ, 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 theory breaks down. We argue that an arrow of time emergesdoi:10.1088/1126-6708/2007/12/027 fatcat:rv5kgzwpc5ccvct24htses76ay