The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories

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) number of free theory states of wide energy range (or order N) mix under the interaction. As a result the planar perturbation theory breaks down. We argue that an arrow of time emerges and the dual string configuration should be interpreted as a stringy black hole.