Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model

Abstract

In this paper we analyze in detail the next-to-leading order (NLO) of the recently obtained large $N$ expansion for the multi-orientable (MO) tensor model. From a combinatorial point of view, we find the class of Feynman tensor graphs contributing to this order in the expansion. Each such NLO graph is characterized by the property that it contains a certain non-orientable ribbon subgraph (a non-orientable jacket). Furthermore, we find the radius of convergence and the susceptibility exponent of the NLO series for this model. These results represent a first step towards the larger goal of defining an appropriate double-scaling limit for the MO tensor model.

16 pages, 12 figures; minor changes w/r to the previous version, accepted for publication in Annales Henri Poincaré

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Cited by in corpus (1)

• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order