Abstract
We demonstrate that random tensors transforming under rank-5 irreducible representations of mathrm {O}(N) can support melonic large N expansions. Our construction is based on models with sextic (5-simplex) interaction, which generalize previously studied rank-3 models with quartic (tetrahedral) interaction (Benedetti et al. in Commun Math Phys 371:55, 2019. arXiv:1712.00249; Carrozza in JHEP 06:039, 2018. arXiv:1803.02496). Beyond the irreducible character of the representations, our proof relies on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs. Our results provide further evidence that the melonic limit is a universal feature of irreducible tensor models in arbitrary rank.
Highlights
In recent years, tensor models have been shown to admit a specific kind of large N limit, known as the melonic limit [3,4,5]
We demonstrate that random tensors transforming under rank-5 irreducible representations of O(N ) can support melonic large N expansions
Our results provide further evidence that the melonic limit is a universal feature of irreducible tensor models in arbitrary rank
Summary
Tensor models have been shown to admit a specific kind of large N limit, known as the melonic limit [3,4,5]. If we could prove it to be bounded from below, the existence of a large N expansion would immediately follow This conjecture is not true in general: stranded graphs with arbitrarily negative degrees do exist. After proving the existence of the large N expansion, the last step consists in showing that it is dominated by melon diagrams At this stage, one might be tempted to prove the following improved statement: any stranded graph with no melon and no double-tadpole has strictly positive degree. We will implicitly account for such cancellations by mean of Cauchy–Schwarz inequalities which, once the large N expansion has been established, can be used to directly bound the full amplitudes of non-melonic Feynman maps (without having to resort to the stranded representation). Edge of a stranded graph with exactly one traversing strand; see
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