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arXiv · 2605.20913

Chaos-Integrability Transition in the BPS Subspace of the $\mathcal{N}=2$ SYK Model

Leon Miyahara·Shono Shibuya
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Abstract

We study chaos-integrability transition purely within a BPS subspace of a specific supersymmetric model that interpolates between the chaotic $\mathcal{N}=2$ SYK model and an integrable $\mathcal{N}=2$ "commuting" SYK model. Using the framework of BPS chaos, we analyze the spectrum of an operator projected onto the BPS subspace. We numerically find that its spectral statistics exhibit random-matrix behavior near the SYK limit and smoothly transitions to Poisson statistics near the integrable limit. Our results provide a direct example of a chaos-integrability crossover diagnosed solely from BPS states.

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Leon Miyahara, Shono Shibuya. 2026-05-20. Chaos-Integrability Transition in the BPS Subspace of the $\mathcal{N}=2$ SYK Model. https://arxiv.org/abs/2605.20913

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