论文标题
CFT方法的约束操作员的（$β$形式）Hermitian One Matrix型号
CFT approach to constraint operators for ($β$-deformed) hermitian one-matrix models
论文作者
论文摘要
由于（$β$ - 成型的）Hermitian One-Matrix模型可以表示为集成的共形场理论（CFT）期望值，因此我们根据Heisenberg代数的发电机来构造操作员，以使约束可以通过将构造的运算符插入集成的综合值来得出。我们还获得了与派生的约束操作员关联并分析其属性的二阶总导数运算符。我们探讨了派生的约束操作员与某些矩阵模型的$ W $表示之间的内在连接。对于外部场中的高斯Hermitian单矩阵模型，以及$β$ formed的$ n \ times n $复杂矩阵模型，我们研究了整合性，并从其$ w $ prencentations中得出相应的角色扩展。此外，证明了文献中杰克多项式平均值的猜想公式。
Since the ($β$-deformed) hermitian one-matrix models can be represented as the integrated conformal field theory (CFT) expectation values, we construct the operators in terms of the generators of the Heisenberg algebra such that the constraints can be derived by inserting the constructed operators into the integrated expectation values. We also obtain the second order total derivative operators associating with the derived constraint operators and analyze their properties. We explore the intrinsic connection between the derived constraint operators and $W$-representations of some matrix models. For the Gaussian hermitian one-matrix model in the external field and $β$-deformed $N\times N$ complex matrix model, we investigate the superintegrability and derive the corresponding character expansions from their $W$-representations. Moreover a conjectured formula for the averages of Jack polynomials in the literature is proved.
