\(O(N)\) random tensor models. (English) Zbl 1362.83010
Summary: 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.
MSC:
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
| 81T18 | Feynman diagrams |
| 05C30 | Enumeration in graph theory |
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