Replica symmetry breaking in random matrix model: A toy model of wormhole networks

Abstract

We study the replica symmetry breaking (RSB) in the Gaussian Unitary Ensemble (GUE) random matrix model. In the large N limit the RSB occurs at the transition temperature TRSB∼N−2/3. We argue that this transition originates from a landscape of almost degenerate local minima of free energy labeled by Young diagrams. We also discuss a possible implication of our findings for the multiply-coupled Sachdev-Ye-Kitaev models and their holographic dual Jackiw-Teitelboim gravity from the viewpoint of ER=EPR conjecture.