Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 056, 23 pages      arXiv:1512.02087      https://doi.org/10.3842/SIGMA.2016.056
Contribution to the Special Issue on Tensor Models, Formalism and Applications

The Multi-Orientable Random Tensor Model, a Review

Adrian Tanasa abc
a) Univ. Bordeaux, LaBRI, UMR 5800, 351 cours de la Libération, 33400 Talence, France
b) IUF, 1 rue Descartes, 75231 Paris Cedex 05, France
c) H. Hulubei National Institute for Physics and Nuclear Engineering, P.O. Box MG-6, 077125 Magurele, Romania

Received December 08, 2015, in final form June 10, 2016; Published online June 15, 2016

Abstract
After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the $1/N$ expansion and of the large $N$ limit ($N$ being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.

Key words: random tensor models; asymptotic expansions.

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