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arXiv · 1908.07178

Melonic Dominance in Subchromatic Sextic Tensor Models

Shiroman Prakash·Ritam Sinha
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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 \textit{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 $K_{3,3}$) 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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BibTeXRIS

Shiroman Prakash, Ritam Sinha. 2019-08-20. Melonic Dominance in Subchromatic Sextic Tensor Models. https://doi.org/10.1103/physrevd.101.126001

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