Sextic tensor models with O(N)^r symmetry and r<5 have exactly three maximally-single-trace interaction vertices, and each yields a large N limit dominated by (generalized) melonic diagrams.
A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling
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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.
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Melonic Dominance in Subchromatic Sextic Tensor Models
Sextic tensor models with O(N)^r symmetry and r<5 have exactly three maximally-single-trace interaction vertices, and each yields a large N limit dominated by (generalized) melonic diagrams.