  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.
