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

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arxiv 2403.05965 v2 pith:P4UPMDCD submitted 2024-03-09 hep-th math-phmath.MP

A. Mironov , A. Oreshina , A. Popolitov This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords betadeformedensembleidentitiesrealizationexternalfieldmodels
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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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  1. Phases in WLZZ Matrix Models

    hep-th 2025-07 conditional novelty 6.0 of 10

    For WLZZ two-matrix models, integration contours describe only a finite-N subspace of Ward identity solutions, and the full solution space is recovered only in the N-to-infinity limit.

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