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. 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.

15 pages; v2: typos corrected, references added, v3: minor corrections, references added

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• JT gravity as a matrix integral
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• Free Energy from Replica Wormholes
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Decoherence in Conformal Field Theory
• Spectral form factor in the double-scaled SYK model
• Low-temperature entropy in JT gravity
• $T\overline{T}$-deformed free energy of the Airy model
• Quenched free energy in random matrix model
• Revealing nonperturbative effects in the SYK model
• Gas of baby universes in JT gravity and matrix models
• A Black Hole Airy Tail
• Replicas for Random Matrices
• Quenched free energy from spacetime D-branes