W-representations of the fermionic matrix and Aristotelian tensor models

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.

arXiv comment20 pages. Revised version accepted for publication in Nuclear Physics B

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Cited by in corpus (3)

• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• Bilinear character correlators in superintegrable theory