W-representations of the fermionic matrix and Aristotelian tensor models

TL;DR

This paper develops W-representations for fermionic matrix and tensor models, deriving Virasoro constraints, character expansions, and connecting them to integrable hierarchies, thus advancing the understanding of their algebraic structures.

Contribution

It introduces W-representations for fermionic matrix and tensor models, including Virasoro constraints and character expansions, linking these models to integrable systems.

Findings

Fermionic matrix model realized via W-representation.

Virasoro constraints form Witt and null 3-algebra.

Partition function's character expansion derived from constraints.

Abstract

We show that the fermionic matrix model can be realized by $W$-representation. We construct the Virasoro constraints with higher algebraic structures, where the constraint operators obey the Witt algebra and null 3-algebra. The remarkable feature is that the character expansion of the partition function can be easily derived from such Virasoro constraints. It is a $\tau$-function of the KP hierarchy. We construct the fermionic Aristotelian tensor model and give its $W$-representation. Moreover, we analyze the fermionic red tensor model and present the $W$-representation and character expansion of the partition function.