Superintegrability of Kontsevich matrix model
Superintegrability of Kontsevich matrix model
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DOI：
10.1140/epjc/s10052-021-09030-x
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发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
A. Mironov;A. Morozov
中科院分区：
文献类型：
--
作者：
A. Mironov;A. Morozov
许多特征值矩阵模型拥有一个特殊的基础，具有明确可计算的平均值的观测。这种显式的可计算性是比普通可积性更强的特征，就像二次势和库仑势在其他中心势中的区别一样，我们称之为超可积性。作为矩阵模型的一个特殊性，相关的基由Schur多项式（特征）及其推广形成，超可积性看起来像是一个性质。这是已知的发生在最重要的情况下，厄米特，酉，和复杂的矩阵模型。在这里，我们增加了两个主要的重要性，其中模型依赖于外部场的例子：一个特殊版本的复杂模型和立方Kontsevich模型。在前一种情况下，简单是对复张量模型的推广。在后一种情况下，相关的字符是celebratedQSchur函数出现在描述自旋Hurwitz数和其他相关的背景。
Many eigenvalue matrix models possess a peculiar basis of observables that have explicitly calculable averages. This explicit calculability is a stronger feature than ordinary integrability, just like the cases of quadratic and Coulomb potentials are distinguished among other central potentials, and we call itsuperintegrability. As a peculiarity of matrix models, the relevant basis is formed by the Schur polynomials (characters) and their generalizations, and superintegrability looks like a property. This is already known to happen in the most important cases of Hermitian, unitary, and complex matrix models. Here we add two more examples of principal importance, where the model depends onexternal fields: a special version of complex model and the cubic Kontsevich model. In the former case, straightforward is a generalization to the complex tensor model. In the latter case, the relevant characters are the celebratedQSchur functions appearing in the description of spin Hurwitz numbers and other related contexts.