Complete solution to Gaussian tensor model and its integrable properties

• Main Authors: H. Itoyama, A. Mironov, A. Morozov
• Format: Article
• Language: English
• Published: Elsevier 2020-03-01
• Series: Physics Letters B
• Online Access: http://www.sciencedirect.com/science/article/pii/S0370269320300411

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.