Size Operator and Spectral Clustering in the Two Coupled SYK Model

• URL: http://arxiv.org/abs/2608.02696v1
• Date: Mon, 03 Aug 2026 11:03:58 GMT
• Title: Size Operator and Spectral Clustering in the Two Coupled SYK Model
• Abstract summary: We show that at finite $N$ the spectrum organizes into clusters labeled by operator size.<n>Low-size clusters evolve into the conformal towers and define a weak-ergodicity-breaking subspace.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: At large $N$, two coupled Sachdev-Ye-Kitaev models realize an eternal traversable wormhole with a discrete spectrum. We show that at finite $N$ the spectrum organizes into clusters labeled by operator size. Low-size clusters evolve into the conformal towers and define a weak-ergodicity-breaking subspace responsible for the long-lived wormhole revival dynamics. Moreover, the competition between size energy and size entropy provides a microscopic interpretation of the wormhole-black hole transition. These results reveal operator size as the bridge between the finite-$N$ spectrum and the emergent gravitational physics at large $N$.

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