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

Matti Raasakka; Adrian Tanasa

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

High Energy Physics - Theory 2015-03-30 v2 General Relativity and Quantum Cosmology Mathematical Physics math.MP

Authors: Matti Raasakka , Adrian Tanasa

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.

Keywords

large $N$ expansion multi-orientable tensor model next-to-leading order Feynman tensor graphs non-orientable jacket radius of convergence susceptibility exponent double-scaling limit

Cite

@article{arxiv.1310.3132,
  title  = {Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model},
  author = {Matti Raasakka and Adrian Tanasa},
  journal= {arXiv preprint arXiv:1310.3132},
  year   = {2015}
}

Comments

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

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

Abstract

Keywords

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