Abstract
We study a description of the large N limit of the Sachdev–Ye–Kitaev (SYK) model in terms of quantum mechanics without quenched disorder. Instead of random couplings, we introduce massive scalar fields coupled to fermions, and study a small mass limit of the theory. We show that, under a certain condition, the correlation functions of fermions reproduce those of the SYK model with a temperature dependent coupling constant in the large N limit. We also discuss a supersymmetric generalization of our quantum mechanical model. As a byproduct, we develop an efficient way of estimating the large N behavior of correlators in the SYK model.
Highlights
We study a description of the large N limit of the Sachdev-Ye-Kitaev (SYK) model in terms of quantum mechanics without quenched disorder
We show that our model reproduces essentially the large N limit of the SYK model, J should be replaced by a temperature dependent coupling Jeff
The simple replacement by the harmonic oscillators behaves as the Gaussian quenched disorder due to some special properties of the large N limit of the SYK model
Summary
Under a certain condition, the correlation functions of fermions reproduce those of the SYK model with a temperature dependent coupling constant in the large N limit. We show that our model reproduces essentially the large N limit of the SYK model, J should be replaced by a temperature dependent coupling Jeff .4. The large N behavior of the two and four point correlators of the SYK model are reproduced by our model. The simple replacement by the harmonic oscillators behaves as the Gaussian quenched disorder due to some special properties of the large N limit of the SYK model.
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