N = 0 , 2 $$ \mathcal{N}=\left(0,\ 2\right) $$ SYK, chaos and higher-spins - Cheng Peng (Journal of High Energy Physics, 2018)
Abstract We study a 2-dimensional SYK-like model with N = 0 , 2 $$ \mathcal{N}=\left(0,\ 2\right) $$ 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 ≫ 1, M ≫ 1 limit with μ ≡ M N $$ μ \equiv \frac{M}{N} $$ being a free parameter. Two distinct higher-spin symmetries emerge when the μ 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 μ varies we find the largest Lyapunov exponent of this model to be slightly larger than that in models with non-chiral supersymmetry.