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arXiv · 1512.06718

$O(N)$ Random Tensor Models

Sylvain Carrozza·Adrian Tanasa
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Abstract

We define in this paper a class of three indices 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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Sylvain Carrozza, Adrian Tanasa. 2016-10-10. $O(N)$ Random Tensor Models. https://doi.org/10.1007/s11005-016-0879-x

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