On the structure of Normal Matrix Model
On the structure of Normal Matrix Model
复制标题
论正态矩阵模型的结构
DOI：
10.1007/s002200050420
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
O. Zaboronsky
中科院分区：
文献类型：
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作者：
L. Chau;O. Zaboronsky
研究了正规矩阵模型的结构。我们证明了具有轴对称势的模型的所有关联函数都可以用一个单变量的全纯函数来表示。这一观察结果被用来证明模型的精确可解性。在连续极限下计算了两点关联函数。答案被证明是普遍的，即潜在的独立的规模的变化。结合具有一般多项式势的NMM，我们发展了一个二维自由费米子形式，并构造了一族完全可积的非线性微分方程族，我们称之为扩展的KP（N）族.著名的KP层次结构是这个家族的低维约化。扩展KP（1）方程族包含（2+1）维Burgers方程。（N×N）NMM的配分函数是扩展KP（N）族的τ函数，它关于平面的所有无穷小同态的代数的子代数是不变的。
We study the structure of the normal matrix model (NMM). We show that all correlation functions of the model with an axially symmetric potential can be expressed in terms of a single holomorphic function of one variable. This observation is used to demonstrate the exact solvability of the model. The two-point correlation function is calculated in the continuum limit. The answer is proven to be universal, i.e. potential independent up to a change of the scale. In connection with NMM with a general polynomial potential we have developed a two-dimensional free fermion formalism and constructed a family of completely integrable hierarchies of non-linear differential equations, which we call the extended-KP(N) hierarchies. The well-known KP hierarchy is a lower-dimensional reduction of this family. The extended-KP(1) hierarchy contains the (2+1)-dimensional Burgers equations. The partition function of the (N×N) NMM is the τ function of the extended-KP(N) hierarchy which is invariant with respect to a subalgebra of an algebra of all infinitesimal diffeomorphisms of the plane.