Size Operator and Spectral Clustering in the Two Coupled SYK Model

Juan Santos-Suárez; Martí Berenguer; Javier Mas; Alfonso V. Ramallo

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arXiv · 2608.02696

Size Operator and Spectral Clustering in the Two Coupled SYK Model

Juan Santos-Suárez·Martí Berenguer·Javier Mas·Alfonso V. Ramallo

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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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Juan Santos-Suárez, Martí Berenguer, Javier Mas, Alfonso V. Ramallo. 2026-08-03. Size Operator and Spectral Clustering in the Two Coupled SYK Model. https://arxiv.org/abs/2608.02696

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