论文标题
光谱曲线和$ W $ - 矩阵模型的代表
Spectral curves and $W$-representations of matrix models
论文作者
论文摘要
我们解释了如何从矩阵模型的$ {\ cal w} $中提取光谱曲线。它是从$ {\ cal w} $ - 运算符的一部分出现的，该操作员在时间变量中是线性的。以这种方式提取光谱曲线的可能性很重要，因为在某些模型中，矩阵积分尚未可用，并且仍然具有所有重要特征。我们将此推理应用于WLZZ模型的家族，并讨论为家庭参数$ n $的非负值而出现的其他特点，当模型取决于其他耦合（双重时间）。在这种情况下，拓扑与$ 1/n $扩展之间的关系破裂。另一方面，所有WLZZ分区函数都是Toda晶格层次结构的$τ$ - 功能，这些模型还庆祝了共同性属性。
We explain how the spectral curve can be extracted from the ${\cal W}$-representation of a matrix model. It emerges from the part of the ${\cal W}$-operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply this reasoning to the family of WLZZ models and discuss additional peculiarities which appear for the non-negative value of the family parameter $n$, when the model depends on additional couplings (dual times). In this case, the relation between topological and $1/N$ expansions is broken. On the other hand, all the WLZZ partition functions are $τ$-functions of the Toda lattice hierarchy, and these models also celebrate the superintegrability properties.
