Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry

Abstract

It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results to the last irreducible $O(N)$ tensor representation available in this context, which carries a two-dimensional representation of the symmetric group $S_3$. Along the way, we emphasize the role of the irreducibility condition: it prevents the generation of vector modes which are not compatible with the large $N$ scaling of the tensor interaction. This example supports the conjecture that a melonic large $N$ limit should exist more generally for higher rank tensor models, provided that they are appropriately restricted to an irreducible subspace.

17 pages, 7 figures

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• Towards background independent quantum gravity with tensor models
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• On the large $D$ expansion of Hermitian multi-matrix models
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Melonic Turbulence
• Diagrammatic proof of the large $N$ melonic dominance in the SYK model
• On the large N limit of the Schwinger-Dyson equation of tensor field theory
• Diagrammatics of the quartic $O(N{)}^3$-invariant Sachdev-Ye-Kitaev-like tensor model
• A Renormalizable SYK-type Tensor Field Theory
• Double scaling limit of multi-matrix models at large $D$
• Stochastic dynamics for Group Field Theories
• Duality of Orthogonal and Symplectic Random Tensor Models: General Invariants
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• Duality of O(N) and Sp(N) random tensor models: tensors with symmetries
• Can we make sense out of "Tensor Field Theory"?