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O(N) Random Tensor Models

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Abstract

We define in this paper a class of three-index tensor models, endowed with \({O(N)^{\otimes 3}}\) invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.

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Authors and Affiliations

  1. Univ. Bordeaux, LaBRI, UMR 5800, 33400, Talence, France

    Sylvain Carrozza & Adrian Tanasa

  2. H. Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125, Magurele, Romania

    Adrian Tanasa

  3. IUF, 1 rue Descartes, 75231, Paris Cedex 05, France

    Adrian Tanasa

Authors
  1. Sylvain Carrozza
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  2. Adrian Tanasa
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Correspondence to Sylvain Carrozza.

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Carrozza, S., Tanasa, A. O(N) Random Tensor Models. Lett Math Phys 106, 1531–1559 (2016). https://doi.org/10.1007/s11005-016-0879-x

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  • DOI: https://doi.org/10.1007/s11005-016-0879-x

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