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 Renormalizable SYK-type Tensor Field Theory
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abstract
In this paper we introduce a simple field theoretic version of the Carrozza-Tanasa-Klebanov-Tarnopolsky (CTKT) "uncolored" holographic tensor model. It gives a more familiar interpretation to the previously abstract modes of the SYK or CTKT models in terms of momenta. We choose for the tensor propagator the usual Fermionic propagator of condensed matter, with a spherical Fermi surface, but keep the CTKT interactions. Hence our field theory can also be considered as an ordinary condensed matter model with a non-local and non-rotational invariant interaction. Using a multiscale analysis we prove that this field theory is just renormalizable to all orders of perturbation theory in the ultraviolet regime.
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2019 1verdicts
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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.