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arXiv · 2403.05965

Two $\beta$-ensemble realization of $\beta$-deformed WLZZ models

A. Mironov·A. Oreshina·A. Popolitov
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Abstract

We consider a two $\beta$-ensemble realization of the series of $\beta$-deformed WLZZ matrix models. We demonstrate that such a realization involves $\beta$-deformed Harish-Chandra-Itzykson-Zuber integrals, one of them providing a coupling to the external field. We also construct Ward identities in the corresponding two $\beta$-ensemble model, which requires a set of identities for partition function of the one $\beta$-ensemble in the external field, and a set of identities for the $\beta$-deformed Itzykson-Zuber integral. These both sets of identities are formulated in terms of the Dunkl operators.

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A. Mironov, A. Oreshina, A. Popolitov. 2024-03-09. Two $\beta$-ensemble realization of $\beta$-deformed WLZZ models. https://doi.org/10.1140/epjc%2Fs10052-024-13067-z

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