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

TL;DR

This paper explores how quantum gravity in AdS spacetime relates to large N Yang-Mills theories, revealing non-perturbative effects at high temperatures that lead to an emergent arrow of time and black hole interpretation.

Contribution

It demonstrates that at high temperatures, large N Yang-Mills theories exhibit non-perturbative mixing of states, causing the breakdown of planar perturbation theory and suggesting a stringy black hole dual.

Findings

Exponential mixing of states in the high-temperature phase.

Breakdown of planar perturbation theory at nonzero coupling.

Emergence of an arrow of time and black hole interpretation.

Abstract

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 $\lambda$, 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 theory breaks down. We argue that an arrow of time emerges and the dual string configuration should be interpreted as a stringy black hole.