Correlators in two rainbow tensor and complex multi-matrix models

TL;DR

This paper develops two rainbow tensor models with rank-3 tensors, providing new formulas for gauge-invariant operators, correlators, and establishing connections with Hurwitz numbers and colored Dessins, also relating to complex multi-matrix models.

Contribution

It introduces new rainbow tensor models, derives their correlator formulas, and links gauge-invariant operators to Hurwitz numbers and Dessins, expanding the mathematical framework of tensor models.

Findings

Derived compact correlator expressions for rainbow tensor models

Established a correspondence between operators and colored Dessins

Connected tensor models to Hurwitz number counting

Abstract

We construct two rainbow tensor models with multi-tensors of rank-$3$ and present their $W$-representations. We give the formula of counting number of independent gauge-invariant operators in terms of Hurwitz numbers and establish a one-to-one correspondence between connected operators and colored Dessins. By means of the colored Dessins and $W$-representations, respectively, we derive two compact expressions of correlators for each of rainbow tensor models. Furthermore, two complex multi-matrix models from the degradations of the constructed rainbow tensor models are also discussed.