W-representations of two-matrix models with infinite set of variables

Article Astronomy & Astrophysics

On KP-integrable skew Hurwitz Τ-functions and their β-deformations

A. Mironov et al.

Summary: This paper extends the old formalism of cut-and-join operators in the theory of Hurwitz tau-functions to describe a wide family of KP-integrable skew Hurwitz tau-functions, including the newly discovered interpolating WLZZ models. It provides detailed proofs, a generalization to a multi-matrix representation, and proposes the beta-deformation of the matrix model. The general interpolating WLZZ model is generated by a W-representation given by a sum of operators from a one-parametric commutative sub-family, with different commutative families related by cut-and-join rotations, where some specific families correspond to well-known Hamiltonians.

PHYSICS LETTERS B (2023)

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Article Physics, Particles & Fields

Interpolating matrix models for WLZZ series

A. Mironov et al.

Summary: We propose a two-matrix model with three sets of parameters that can interpolate between various models. These models are defined through W-representations and have integrable properties described by skew hyper-geometric t-functions. We also discuss generalizations of the WLZZ models realized by W-representations associated with infinite commutative families of generators of w8-algebra.

EUROPEAN PHYSICAL JOURNAL C (2023)

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Article Physics, Particles & Fields

On W-operators and superintegrability for dessins d'enfant

Alexander Alexandrov

Summary: In this short note, we establish a connection between a family of partition functions introduced by Wang, Liu, Zhang, and Zhao and certain specializations of the generating function for dessins d'enfant. This connection leads to a new W-description for orbifold strongly monotone Hurwitz numbers and new examples of superintegrability in matrix models.

EUROPEAN PHYSICAL JOURNAL C (2023)

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Article Physics, Particles & Fields

Superintegrability for (β-deformed) partition function hierarchies with W-representations

Rui Wang et al.

Summary: We construct partition function hierarchies using W-representations and analyze their superintegrability properties. Character expansions with respect to Schur functions and Jack polynomials are derived. The constructed hierarchies include well-known superintegrable matrix models.

EUROPEAN PHYSICAL JOURNAL C (2022)

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Article Physics, Particles & Fields

W-representations of the fermionic matrix and Aristotelian tensor models

Lu-Yao Wang et al.

Summary: In this study, the fermionic matrix model and tensor model are investigated in the context of W-representation and higher algebraic structures. By utilizing Virasoro constraints, the character expansion of the partition function can be derived, revealing its nature as a Tau-function of the KP hierarchy.

NUCLEAR PHYSICS B (2021)

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Article Astronomy & Astrophysics