Conformal invariance and superstring theory

共形不变性和超弦理论

• 批准号: 01540237
• 负责人: SAKAI Norisuke
• 金额: $ 1.6万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540237/
• 关键词: conformal invariance; supersting theory; operator product expansion; matrix model; two-dimensional gravity; Liouville field; area-preserving diffeomorphism; supersymmetry; ビランロ代数; 非摂動的効果; W代数; ビラソロ代数; チャ-ン・サイモン・ゲ-ジ理論; ウェス・ズミノ模型; カラビ・ヤオ空間

Superstring Theory is the most promising candidate for a unified theory including gravity. The most basic principle underlying the superstring theory is the conformal invariance in the two-dimensional world sheet. The conformal invariance also plays a crucial role in classifying the second order phase transition in statistical physics in two demensions. Recent progress in matrix models provides a powerful non perturbative treatment of two-dimensional gravity form the viewpoint of discretized theory. Continuum approach based on the Liouville field theory is complementary and particularly useful in revealing physical content.We have studied the conformal field theory coupled to two-dimensional gravity using the continuum approach. We have succeeded to analyze the partition function and correlation functions in the case of conformal matter with the unit central charge. This case is especially interesting from the viewpoint of string therory, since it allows a space-time interpretalon in the usual sense. We have found that the operator product expansion is very useful in unraveling the singularity structure of the two-dimensional gravity coulpled with the conformal matter. We are also studying the coupling of physical states using the symmetry of area-preserving diffeomorphisms.

超弦理论是包含引力的统一理论最有希望的候选者。超弦理论最基本的原理是二维世界图的共形不变性。保形不变性在二维统计物理的二阶相变分类中也起着至关重要的作用。从离散化理论的角度出发，矩阵模型的最新进展为二维重力提供了一种强有力的非微扰处理方法。基于刘维尔场论的连续体方法是互补的，在揭示物理内容方面特别有用。用连续介质方法研究了二维重力耦合的共形场论。我们成功地分析了具有单位中心电荷的共形物质的配分函数和相关函数。从弦理论的观点来看，这种情况特别有趣，因为它允许通常意义上的时空解释。我们发现，算子积展开对于揭示二维重力与保形物质耦合的奇异结构是非常有用的。我们还利用保面积微分同态的对称性研究了物理状态的耦合。

项目成果

Y. Saitoh: "Bosonic Constructions of W3 Algebra" Prog. Theor. Phys.83 [3]. 621-637 (1990)

Y. Saitoh：“W3 代数的玻色子构造”Prog。

N.Sakai: "A Compact Boson Coupled to TwoーDimensional Gravity" Int.J.Mod.Phys.6. 2743-2754 (1991)

N.Sakai：“耦合到二维引力的紧凑玻色子”Int.J.Mod.Phys.6 2743-2754 (1991)

N.sakai: "String Loop Corrections from Fusion of Handles and Vertex Operators" Phys.Lett.B197. 109-114 (1987)

N.sakai：“句柄和顶点运算符融合的字符串循环校正”Phys.Lett.B197。

N.Sakai: "Correlation Functions of c=1 Matter Coupled to Two-Dimensional Gravity" Prog.Theor.Phys.86. 547-553 (1991)

N.Sakai：“c=1 物质与二维重力耦合的相关函数”Prog.Theor.Phys.86。

N.Sakai: "Factorization and Topological Statets in c=1 Matter Coupled to 2-D Gravity" Phys.Lett.

N.Sakai：“c=1 物质与二维重力耦合的因式分解和拓扑状态”Phys.Lett。