Theory of Two-Dimensional Black Hole

二维黑洞理论

基本信息

批准号：
05640331
负责人：
EGUCHI Tohru
金额：
$ 0.83万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

项目摘要

Topolgical field theory is an attempt at understanding the geometrical principles behind the string theory and is currently under active investigations. It is known that an N=2 supersymmetric non-linear sigma-model can be suitably twisted and converted into a topological field theory, topological sigma-model. The partition function of the topological sigma-model is given by the sum over holomorphic maps onto some target space and in general difficult to evaluate. Eguchi, together with S.K.Yang, studied the topological CP^1 model on an arbitrary Riemann surfaces and have shown that the integrable structure of the system is described by the 1-dimensional Toda hierarchy and its partition function can be precisely represented in terms of some large-N matrix integral.The c=1 string theory was originally introduced as an 1-dimensional matrix quantum mechanics and has further been studied extensively using the moethod of collective coordinates, free fermions etc.. Recently an interpretation of the c=1 string theory as a topological field theory has been proposed and a Landau-Ginzburg description has been introduced. Eguchi, together with H.Kanno, studied this proposal and have shown that the integrable structrue of the theory is given by the Toda lattice hierarchy with a special constraint condition being imposed.Eguchi, togetehr with Y.Yamada and S.K.Yang, studied the higher genus structure of the topological string theory based on the analysis of the higher order corrections to the flow equations. It was shown that there are models of topological string theories which are cosistent at genus g=0 and 1 but can not be extended into higher genera g<greater than or

托管场理论是一种尝试理解字符串理论背后的几何原理的尝试，目前正在积极研究中。众所周知，n = 2超对称非线性sigma模型可以适当地扭曲并转化为拓扑场理论，即拓扑sigma-Model。拓扑Sigma模型的分区函数由整体图上的总和到某些目标空间，通常难以评估。 Eguchi与S.K. Yang一起在任意的Riemann表面上研究了拓扑CP^1模型，并表明，该系统的整合结构由1维TODA层次结构及其分区函数描述，并且其分区函数可以通过某些大型N Matrix的整合来准确地代表C = 1量的量子。广泛地使用集体坐标，自由费米子等的莫雷德。最近提出了对C = 1字符串理论作为拓扑场理论的解释，并引入了Landau-Ginzburg的描述。 Eguchi与H.Kanno一起研究了这一建议，并表明，该理论的整合结构是由Toda Lattice层次结构给出的，并强加了特殊的约束条件。Eguchi，togetehr togetehr y.Yamada和s.k.yang，研究了基于更高的静态弦乐结构的较高阶段理论的阶级方程式，以进行较高的阶段方程式。结果表明，有一些拓扑弦理论模型在g = 0和1处具有共识，但不能扩展到更高的属g <g <大于或大的属。