We study a 2-dimensional SYK-like model with \( \mathcal{N}=\left(0,\ 2\right) \) 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 $$\gg$$ 1, M$$\gg$$ 1 limit with \( \mu \equiv \frac{M}{N} \) 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.
Peng, Cheng (2018). $\mathcal{N}=\left(0, 2\right)$ SYK, chaos and higher-spins. Journal of High Energy Physics (Online), 2018(12). https://doi.org/10.1007/jhep12(2018)065
Peng, Cheng, "$\mathcal{N}=\left(0, 2\right)$ SYK, chaos and higher-spins," Journal of High Energy Physics (Online) 2018, no. 12 (2018), https://doi.org/10.1007/jhep12(2018)065
@article{osti_1611328,
author = {Peng, Cheng},
title = {$\mathcal{N}=\left(0, 2\right)$ SYK, chaos and higher-spins},
annote = {We study a 2-dimensional SYK-like model with \( \mathcal{N}=\left(0,\ 2\right) \) 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 $\gg$ 1, M$\gg$ 1 limit with \( \mu \equiv \frac{M}{N} \) 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.},
doi = {10.1007/jhep12(2018)065},
url = {https://www.osti.gov/biblio/1611328},
journal = {Journal of High Energy Physics (Online)},
issn = {ISSN 1029-8479},
number = {12},
volume = {2018},
place = {United States},
publisher = {Springer Berlin},
year = {2018},
month = {12}}
Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)https://doi.org/10.22323/1.318.0218