Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps

Abstract

Ordinary tensor models of rank $D\ge 3$ 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.

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Cited by in corpus (7)

• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• A power counting theorem for a $p^{2a}{\varphi }^4$ tensorial group field theory
• Aspects of quantum gravity
• Another proof of the $1/N$ expansion of the rank three tensor model with tetrahedral interaction
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Quartic Tensor Models
• Constraint algebra of general relativity from a formal continuum limit of canonical tensor model