Random tensor models—theO(N)3-invariant model

Abstract

AbstractWe define in this chapter a class of tensor models endowed with O(N)3-invariance, N being again 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 the U(N)3-invariant models treated in the previous two chapters. We first exhibit the existence of a large N expansion for such a model with general interactions (non-necessary quartic). We then focus on the quartic model and we identify the leading order and next-to-leading Feynman graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the so-called critical exponents. This is achieved through the use of various analytic combinatorics techniques.