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

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.

High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2605.20913 [hep-th]

(or arXiv:2605.20913v2 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2605.20913 Focus to learn more arXiv-issued DOI via DataCite

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