The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three

Abstract

We prove rigorously that the symmetric traceless and the antisymmetric tensor models in rank three with tetrahedral interaction admit a $1/N$ expansion, and that at leading order they are dominated by melon diagrams. This proves the recent conjecture of I. Klebanov and G. Tarnopolsky in JHEP 10 (2017) 037 [arXiv:1706.00839], which they checked numerically up to 8th order in the coupling constant.

40 pages, many figures

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• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Combinatorial aspects of the Sachdev-Ye-Kitaev model
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Melonic Dominance in Subchromatic Sextic Tensor Models
• On the large $D$ expansion of Hermitian multi-matrix models
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Melonic Turbulence
• Maximizing the number of edges in three-dimensional colored triangulations whose building blocks are balls
• On the large N limit of the Schwinger-Dyson equation of tensor field theory
• Diagrammatics of the quartic $O(N{)}^3$-invariant Sachdev-Ye-Kitaev-like tensor model
• Complete Solution of a Gauged Tensor Model
• Double scaling limit of multi-matrix models at large $D$
• Stochastic dynamics for Group Field Theories
• A Solvable Tensor Field Theory
• Duality of Orthogonal and Symplectic Random Tensor Models: General Invariants
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• Tensor models with generalized melonic interactions
• Sextic tensor field theories in rank $3$ and $5$
• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Another proof of the $1/N$ expansion of the rank three tensor model with tetrahedral interaction
• Tensor Field Theories: Renormalization and Random Geometry
• 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
• The Tensor Track VII: From Quantum Gravity to Artificial Intelligence
• Melonic large $N$ limit of $5$-index irreducible random tensors
• Can we make sense out of "Tensor Field Theory"?