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

TL;DR

This paper investigates the transition from chaos to integrability within a BPS subspace of an $ ext{N}=2$ supersymmetric SYK model, demonstrating a spectral transition from random-matrix to Poisson statistics.

Contribution

It provides a novel analysis of chaos-integrability crossover using BPS states in a supersymmetric model, bridging chaotic and integrable regimes.

Findings

Spectral statistics shift from random-matrix to Poisson near the integrable limit.

BPS chaos framework effectively diagnoses chaos-integrability transition.

Numerical results confirm a smooth spectral transition in the 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.