Topological $\sigma$-Models and Large-$N$ Matrix Integral
Topological $\sigma$-Models and Large-$N$ Matrix Integral
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拓扑$sigma$模型和大$N$矩阵积分
DOI：
10.1142/s0217751x95001959
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发表时间：
1995
影响因子：
1.6
通讯作者：
Sung
中科院分区：
文献类型：
--
作者：
T. Eguchi;K. Hori;Sung
在本文中，我们详细描述了表示的拓扑CP 1模型的矩阵积分，我们已经介绍了在以前的文章。我们首先讨论的可积结构的CP 1模型，并表明，它是由一维户田层次的扩展。然后，我们引入了一个矩阵模型，它再现了从任意黎曼曲面到CP 1的全纯映射的总和。我们用几何方法计算了曲线模空间上的交数，结果表明与矩阵模型预测的结果一致。我们还开发了一个Landau-Ginzburg（LG）描述的CP 1模型使用超势eX + et 0，Qe-X给出的Lax算子的户田层次（X是LG场和t0，Q是耦合常数的Kahler类）。超势的形式表明CP 1和N=2超对称sine-Gordon理论之间的密切联系，这是由几位作者在不久前指出的。我们还讨论了我们的建设可能的推广到其他流形，并提出了LG制定的拓扑CP 2模型。
In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP1 model and show that it is governed by an extension of the one-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP1. We compute intersection numbers on the moduli space of curves using a geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the CP1 model using a superpotential eX + et0,Q e-X given by the Lax operator of the Toda hierarchy (X is the LG field and t0,Q is the coupling constant of the Kahler class). The form of the superpotential indicates the close connection between CP1 and N=2 supersymmetric sine-Gordon theory which was noted sometime ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present an LG formulation of the topological CP2 model.