W-representation of Rainbow tensor model

TL;DR

This paper extends the W-representation framework to the rainbow tensor model, deriving Virasoro constraints, algebraic structures, and explicit correlator formulas, with applications to various tensor models including non-Gaussian cases.

Contribution

It generalizes the W-representation method from matrix models to rainbow tensor models, revealing algebraic structures and providing explicit correlator expressions.

Findings

Virasoro constraints obey Witt and null 3-algebra

Explicit correlator formulas for several tensor models

Dual expression for non-Gaussian red tensor model

Abstract

We analyze the rainbow tensor model and present the Virasoro constraints, where the constraint operators obey the Witt algebra and null 3-algebra. We generalize the method of W-representation in matrix model to the rainbow tensor model, where the operators preserving and increasing the grading play a crucial role. It is shown that the rainbow tensor model can be realized by acting on elementary function with exponent of the operator increasing the grading. We derive the compact expression of correlators and apply it to several models, i.e., the red tensor model, Aristotelian tensor model and r=4 rainbow tensor model. Furthermore, we discuss the case of the non-Gaussian red tensor model and present a dual expression for partition function through differentiation.