Abstract
It has recently been proven that in rank three tensor models, the antisymmetric and symmetric traceless sectors both support a large N expansion dominated by melon diagrams [1]. 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 S3. 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.
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Carrozza, S. Large N limit of irreducible tensor models: O(N) rank-3 tensors with mixed permutation symmetry. J. High Energ. Phys. 2018, 39 (2018). https://doi.org/10.1007/JHEP06(2018)039
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DOI: https://doi.org/10.1007/JHEP06(2018)039