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

References in corpus (13)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• The complete $1/N$ expansion of a SYK--like tensor model
• On KP-integrable Hurwitz functions
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• On Factorization of Generalized Macdonald Polynomials

Cited by in corpus (1)

• The Non-melonic Sector of Tensor Models and Gravity