The 1/N Expansion of Multi-Orientable Random Tensor Models

Abstract

Multi-orientable group field theory (GFT) was introduced in Tanasa (J Phys A 45:165401, 2012), as a quantum field theoretical simplification of GFT, which retains a larger class of tensor graphs than the colored one. In this paper we define the associated multi-orientable identically independent distributed multi-orientable tensor model and we derive its 1/N expansion. In order to obtain this result, a partial classification of general tensor graphs is performed and the combinatorial notion of jacket is extended to the m.o. graphs. We prove that the leading sector is given, as in the case of colored models, by the so-called melon graphs. © 2013 Springer Basel.