$\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins

TL;DR

This paper analyzes a 2D $ abla$=(0,2) supersymmetric SYK model, revealing emergent higher-spin symmetries and chaos suppression at parameter extremes, thus linking SYK models with higher-spin theories.

Contribution

It provides an analytical and numerical study of a 2D $ abla$=(0,2) supersymmetric SYK model, demonstrating emergent higher-spin symmetries and chaos behavior dependence on parameters.

Findings

Higher-spin symmetries appear at parameter extremes.

Chaotic behavior vanishes at the limits of the parameter range.

Largest Lyapunov exponent slightly exceeds non-chiral supersymmetry models.

Abstract

We study a 2-dimensional SYK model with $\mathcal{N}=(0,2)$ supersymmetry. The model describes $N$ chiral supermultiplets and $M$ Fermi supermultiplets with a $(q+1)$-field interaction. We solve the model analytically and numerically in the $N\gg 1$, $M\gg 1$ limit with $\mu\equiv \frac{M}{N}$ being a free parameter. Two distinct higher-spin symmetries emerge when the $\mu$ parameter approaches the two ends of its range. This is verified by the appearance of conserved higher-spin operators and the vanishing of chaotic behaviors in the two limits. Therefore this model provides a manifest realization of the widely believed connection between SYK-like models and higher-spin theories. In addition, as the parameter $\mu$ varies we find the largest Lyapunov exponent of this model to be slightly larger than that in models with non-chiral supersymmetry. A tensor model without random couplings that shares the same infrared physics is also introduced.