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

## TL;DR

This paper investigates replica symmetry breaking in a Gaussian Unitary Ensemble random matrix model, revealing a transition at a specific temperature linked to a landscape of local minima, with implications for quantum gravity models.

## Contribution

It introduces a novel analysis of RSB in GUE matrices and connects the transition to a landscape of minima, providing insights relevant to holographic duality and quantum gravity.

## Key findings

- RSB occurs at temperature T_RSB ~ N^{-2/3} in large N limit.
- Transition linked to a landscape of degenerate minima labeled by Young diagrams.
- Implications discussed for Sachdev-Ye-Kitaev models and holographic duality.

## Abstract

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.