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

• DOI: 10.1007/s00023-013-0262-8
• Publication Date: 2013-06-04T21:48:15Z
• Authors: Stéphane Dartois; Vincent Rivasseau; Adrian Tanasa
• Keywords: High Energy Physics - Theory; High Energy Physics - Theory (hep-th); FOS: Mathematics; Mathematics - Combinatorics; FOS: Physical sciences; General Relativity and Quantum Cosmology (gr-qc); Combinatorics (math.CO); General Relativity and Quantum Cosmology

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.<br/>18 pages, 17 figures<br/>