Melonic Dominance in Subchromatic Sextic Tensor Models
Abstract
We study tensor models based on O(N)r symmetry groups constructed out of rank-r tensors with order-q interaction vertices. We refer to those tensor models for which r<q-1 as subchromatic. We focus most of our attention on sextic (q=6) models with maximally-single-trace interactions. We show that only three subchromatic sextic maximally-single-trace interaction vertices exist: these are the r=3 prism, the r=3 wheel (or K3,3) and the r=4 octahedron. For theories based on these interactions we demonstrate that the set of Feynman diagrams that contribute to the free energy in the large N limit are melonic (or closely related to melonic diagrams, in the case of the prism) and thus can be explicitly summed.
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