论文标题
一维拓扑重力的两矩阵模型扩展
Noncommutativity in two-matrix model extension of one-dimensional topological gravity
论文作者
论文摘要
一维拓扑重力定义为高斯积分作为其分区函数。高斯积分提供玩具模型，作为一个更简单的单矩阵模型，众所周知，可以提供二维拓扑引力的描述。一维拓扑引力与二维拓扑重力继承了可集成的层次结构，但它是汉堡层次结构，而不是korteweg-de vries层次结构。利用这一事实，研究了一维拓扑引力的扩展到两个矩阵模型的类似物，并显示了相关的分区函数由一维拓扑引力的一对分区函数组成，该功能通过Moyal-weyl-weyl产品交织在一起，该功能可以为其自由度提供evellicit Formula ulage。扩展系统显示了一个层次结构，该结构解释为汉堡层次结构的非交换性扩展。提出了与非交通性u（1）规格理论的关系。
One-dimensional topological gravity is defined as a Gaussian integral as its partition function. The Gaussian integral supplies a toy model as a simpler version of one-matrix model that is well known to provide a description of two-dimensional topological gravity. The one-dimensional topological gravity inherits an integrable hierarchy structure as with two-dimensional topological gravity, yet it is the Burgers hierarchy rather than the Korteweg--de Vries hierarchy. Making use of this fact, an extension of the one-dimensional topological gravity to an analogue of two-matrix model is investigated and the associated partition function is shown to consist of a pair of partition functions of one-dimensional topological gravity intertwined via the Moyal--Weyl product, which enables to provide an explicit formula for its free energy. The extended system shows a hierarchy structure interpreted as a noncommutative extension of the Burgers hierarchy. The relation to noncommutative U(1) gauge theory is suggested.
