The Multi-Orientable Random Tensor Model, a Review

Abstract

After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the $1/N$ expansion and of the large $N$ limit ($N$ being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.

References in corpus (5)

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• The double scaling limit of the multi-orientable tensor model
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Cited by in corpus (32)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Spectra of Operators in Large $N$ Tensor Models
• Invitation to Random Tensors
• Ward identities and combinatorics of rainbow tensor models
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Symmetry Breaking in Coupled SYK or Tensor Models
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• Large $N$ Limits in Tensor Models: Towards More Universality Classes of Colored Triangulations in Dimension $d\ge 2$
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• Conformality of $1/N$ corrections in SYK-like models
• The full Ward-Takahashi Identity for colored tensor models
• Tensor Models for Black Hole Probes
• On the large $D$ expansion of Hermitian multi-matrix models
• Hagedorn Temperature in Large $N$ Majorana Quantum Mechanics
• Surgery in colored tensor models
• Diagrammatics of the quartic $O(N{)}^3$-invariant Sachdev-Ye-Kitaev-like tensor model
• On the large N limit of the Schwinger-Dyson equation of tensor field theory
• Diagrammatic proof of the large $N$ melonic dominance in the SYK model
• Double scaling limit of the prismatic tensor model
• Double scaling limit of multi-matrix models at large $D$
• $(D+1)$-Colored Graphs - a Review of Sundry Properties
• Tensor models with generalized melonic interactions
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• Another proof of the $1/N$ expansion of the rank three tensor model with tetrahedral interaction
• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Duality of O(N) and Sp(N) random tensor models: tensors with symmetries
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Tensor Field Theories: Renormalization and Random Geometry
• Triangle-hinge models for unoriented membranes