O(N) Random Tensor Models

• DOI: 10.1007/s11005-016-0879-x
• Publication Date: 2016-08-18T07:48:59Z
• Authors: Sylvain Carrozza; Adrian Tanasa
• Keywords: High Energy Physics - Theory; model: tensor; analytic combinatorics.; [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]; Feynman graph; [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]; colored graphs; FOS: Physical sciences; critical phenomena; Mathematical Physics (math-ph); O(N); [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]; field theory; 01 natural sciences; U(N); 83C27, 81T18, 05C30; tensor models; High Energy Physics - Theory (hep-th); 0103 physical sciences; [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]; expansion 1/N; Mathematical Physics

23 pages, 14 figures<br/>We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the $U(N)$ invariant models. We first exhibit the existence of a large $N$ expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large $N$ expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.<br/>