\(O(N)\) random tensor models

DOI10.1007/S11005-016-0879-XzbMATH Open1362.83010arXiv1512.06718OpenAlexW3100967813MaRDI QIDQ2397802

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Publication date: 23 May 2017

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Abstract: We define in this paper a class of three indices tensor models, endowed with $O(N{)}^{otimes3}$ 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.

Full work available at URL: https://arxiv.org/abs/1512.06718

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