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

Understand

We study the replica symmetry breaking (RSB) in the Gaussian Unitary Ensemble (GUE) random matrix model.

• We find that the RSB occurs at the transition temperature $T_{\text{RSB}}\sim N^{-2/3}$ in the large $N$ limit.
• 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.