Melonic large \(N\) limit of \(5\)-index irreducible random tensors. (English) Zbl 1487.81125
Summary: 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 (D. Benedetti et al. [Commun. Math. Phys. 371, No. 1, 55–97 (2019; Zbl 1425.81071)]; S. Carrozza [J. High Energy Phys. 2018, No. 6, Paper No. 39, 21 p. (2018; Zbl 1395.81155)]). 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.
MSC:
| 81T10 | Model quantum field theories |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 60B20 | Random matrices (probabilistic aspects) |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81T18 | Feynman diagrams |
| 03F60 | Constructive and recursive analysis |
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