Liouville Field Theory — A decade after the revolution
Liouville Field Theory — A decade after the revolution
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刘维尔场论——革命十年后
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Y. Nakayama
中科院分区：
文献类型：
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作者：
Y. Nakayama
我们回顾了刘维场论及其矩阵模型对偶的最新进展（截至2004年1月）。本综述包括三个部分。在第一部分中，我们回顾了玻色子刘维理论。在简要回顾了必要的背景之后，我们讨论了体结构常数（DOZZ公式）和边界态（FZZT膜和ZZ膜）。还介绍了各种应用。在第二部分中，我们回顾了刘维尔理论的超对称扩展。我们首先讨论玻色刘维尔理论中的体结构常数和膜，然后给出矩阵对偶描述及其应用。在第三部分中，刘维理论的无取向表面进行了审查。在引入交叉态后，我们讨论了矩阵模型的对偶描述和蝌蚪相消条件。本文还包括一些原始材料，如从其他已知的对偶中推导出N = 2 Liouville理论的约束对偶作用量，以及Liouville交叉态与c = 0无取向矩阵模型的比较。这是基于我2004年1月提交给东京大学理学部物理学系的硕士论文。
We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master’s thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.