Enhancing non-melonic triangulations: a tensor model mixing melonic and planar maps. (English) Zbl 1329.81258
Summary: Ordinary tensor models of rank \(D \geq 3\) 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.
MSC:
| 81T10 | Model quantum field theories |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 82B30 | Statistical thermodynamics |
| 82D60 | Statistical mechanics of polymers |
| 83C45 | Quantization of the gravitational field |
| 05C05 | Trees |
| 05C80 | Random graphs (graph-theoretic aspects) |
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