Melonic Large N Limit of 5-Index Irreducible Random Tensors

We demonstrate that random tensors transforming under rank-5 irreducible representations of 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.

Automated summary

We demonstrate that random tensors transforming under rank-5 irreducible representations of O(N) can support melonic large N expansions. Our proof relies on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs.