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The 1/N Expansion of Tensor Models with Two Symmetric Tensors

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Abstract

It is well known that tensor models for a tensor with no symmetry admit a 1/N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/N expansion dominated by melonic graphs.

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Authors and Affiliations

  1. Centre de Physique Théorique, École Polytechnique, CNRS, 91128, Palaiseau, France

    Razvan Gurau

  2. Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, ON, N2L 2Y5, Canada

    Razvan Gurau

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  1. Razvan Gurau
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Correspondence to Razvan Gurau.

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Communicated by X. Yin

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Gurau, R. The 1/N Expansion of Tensor Models with Two Symmetric Tensors. Commun. Math. Phys. 360, 985–1007 (2018). https://doi.org/10.1007/s00220-017-3055-y

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  • DOI: https://doi.org/10.1007/s00220-017-3055-y

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