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arXiv · 2408.02281

Higher order constraints for the ($\beta$-deformed) Hermitian matrix models

Rui Wang
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Abstract

We construct the ($\beta$-deformed) higher order total derivative operators and analyze their remarkable properties. In terms of these operators, we derive the higher order constraints for the ($\beta$-deformed) Hermitian matrix models. We prove that these ($\beta$-deformed) higher order constraints are reducible to the Virasoro constraints. Meanwhile, the Itoyama-Matsuo conjecture for the constraints of the Hermitian matrix model is proved. We also find that through rescaling variable transformations, two sets of the constraint operators become the $W$-operators of $W$-representations for the ($\beta$-deformed) partition function hierarchies in the literature.

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Rui Wang. 2024-08-05. Higher order constraints for the ($\beta$-deformed) Hermitian matrix models. https://doi.org/10.1140/epjc%2Fs10052-024-13377-2

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