2015/02/04 by Valentin Bonzom, Thibault Delepouve, Vincent Rivasseau · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Computer science #Cosmology and Gravitation Theories #Coupling constant #Exponent #Mathematics #Mixing (physics) #Noncommutative and Quantum Gravity Theories #Physics #Planar #Pure mathematics #Quantum mechanics #Quartic function #Rank (graph theory) #Spanning tree #Statistical physics #Tensor (intrinsic definition) #hep-th #math-ph #math.CO #math.MP #msc:81T99
paper · pdf · doi:10.1016/j.nuclphysb.2015.04.004
published as Nuclear Physics B Volume 895, June 2015, Pages 161-191
arxiv created 2015/02/04 · openalex publication_date 2015/04/11 · arxiv updated 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Ordinary tensor models of rank D≥3 are dominated at large N by tree-like graphs, known as melonic triangulations. We here show that non-melonic contributions can be enhanced consistently, leading to different types of large N limits. We first study the most generic quartic model at D=4, with maximally enhanced non-melonic interactions. The existence of the 1/N expansion is proved and we further characterize the dominant triangulations. This combinatorial analysis is then used to define a non-quartic, non-melonic class of models for which the large N free energy and the relevant expectations can be calculated explicitly. They are matched with random matrix models which contain multi-trace invariants in their potentials: they possess a branched polymer phase and a 2D quantum gravity phase, and a transition between them whose entropy exponent is positive. Finally, a non-perturbative analysis of the generic quartic model is performed, which proves analyticity in the coupling constants in cardioid domains.