Abstract
We study a 2-dimensional SYK-like model with mathcal{N}=left(0, 2right) 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 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.
Highlights
The N = (0, 2) supersymmetry plays an important role of this model
It is widely believed that the SYK-like models have close relations with higher-spin theories; higher-spin theories should be thought as a subsector of some tensionless limit of string theory, while the SYK model should be holographically dual to some string theory with finite tension [6]
The operators running in the channel tha is detected by our ladder diagrams (3.1)–(3.9) are all bosonic, so we only look for solutions with integer s, at any q
Summary
We consider 4-point functions of this model. Because there are two different types of multiplets in the model, there will be a few different 4-point correlation functions. As in the 1-dimensional cases [39, 99, 102], the correlation function can be computed either in terms of superfields or component fields. In the rest of the paper we work in the component formalism
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