Complete solution to Gaussian tensor model and its integrable properties

Abstract

Similarly to the complex matrix model, the rainbow tensor models are superintegrable in the sense that arbitrary Gaussian correlators are explicitly expressed through the Clebsh-Gordan coefficients. We introduce associated (Ooguri-Vafa type) partition functions and describe their $W$-representations. We also discuss their integrability properties, which can be further improved by better adjusting the way the partition function is defined. This is a new avatar of the old unresolved problem with non-Abelian integrability concerning a clever choice of the partition function. This is a part of the long-standing problem to define a non-Abelian lift of integrability from the fundamental to generic representation families of arbitrary Lie algebras.

9 pages

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Cited by in corpus (15)

• Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations
• Superintegrability of Kontsevich matrix model
• A slow review of the AGT correspondence
• Quantization of Harer-Zagier formulas
• W-representation of Rainbow tensor model
• W-representations of the fermionic matrix and Aristotelian tensor models
• Harer-Zagier formulas for knot matrix models
• Hook variables: cut-and-join operators and $\tau$-functions
• Genus expansion of matrix models and $\hslash$ expansion of KP hierarchy
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• Superintegrability and Kontsevich-Hermitian relation
• $W$-representations of two-matrix models with infinite set of variables
• Backgrounds from Tensor Models: A Proposal
• The Non-melonic Sector of Tensor Models and Gravity
• Review on the Operator/Feynman diagram/Dessins d'enfant Correspondence in Tensor Model