强耦合极限下非线性西格玛模型的维里展开
Virial expansion of the non-linear sigma model in the strong coupling limit
摘要：
我们发展了一种微扰方法来研究在强耦合极限下具有一般耦合矩阵的超对称非线性西格玛模型。该方法使我们能够显式地计算本征函数和两个层次的关联函数的微扰展开的最低阶的时刻。我们发现，所得到的表达式是等价的相应的随机矩阵系综的结果。这样的等价性阐明和推广到所有阶的微扰扩展映射的西格玛模型到场论描述的几乎对角随机矩阵。
英文摘要：
We develop a perturbative approach to study the supersymmetric non-linear sigma model characterized by a generic coupling matrix in the strong coupling limit. The method allows us to calculate explicitly the moments of the eigenfunctions and the two-level correlation function in the lowest order of the perturbative expansion. We find that the obtained expressions are equivalent to the results derived before for the corresponding random matrix ensembles. Such an equivalence is elucidated and generalized to all orders of the perturbative expansion by mapping the sigma model onto the field theory describing the almost diagonal random matrices.
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