Melonic large $N$ limit of $5$-index irreducible random tensors

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 (arXiv:1712.00249 and 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.