The 1/N expansion of multi-orientable random tensor models

TL;DR

This paper develops a 1/N expansion for multi-orientable tensor models, extending graph classification techniques and identifying melon graphs as the dominant contribution, thus advancing understanding of tensor model behavior.

Contribution

It introduces a 1/N expansion for multi-orientable tensor models and extends graph classification methods to this framework, highlighting the role of melon graphs.

Findings

The 1/N expansion is derived for multi-orientable tensor models.

Melon graphs dominate the leading order sector.

Graph classification techniques are extended to multi-orientable graphs.

Abstract

Multi-orientable group field theory (GFT) has been introduced in A. Tanasa, J. Phys. A 45 (2012) 165401, arXiv:1109.0694, 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 multi-orientable graphs. We prove that the leading sector is given, as in the case of colored models, by the so-called melon graphs.