Analysis of the non-perturbative structure of string theory on the basis of string field theory

本研究的目的是利用弦论的提法--“弦场理论”来研究STING理论中的各种非微扰方面，并对弦场理论本身的提法进行重新思考。我们对三次弦场论和真空弦场论这两种弦场论进行了以下研究：(1)三次弦场论中含时解的分析是围绕不稳定D-膜展开的弦场论。我们研究了表示D-膜衰变过程的含时解的行为。弦场论与普通场论有很大的不同，因为弦场论包含关于时间坐标的无限导数。我们的分析对于理解弦场论特有的性质是重要的。(2)VSFT中依赖于时间的解的构造和分析我们构造并研究了对应于衰变…的依赖于时间的解在VSFT的框架下，更多的是不稳定的D-膜，这是一种围绕没有D-膜的构型扩展的弦场理论。通过使用特别是蒙特卡罗模拟的分析，我们发现很可能存在具有理想轮廓的解。(3)分析D膜经典解周围的VSFT的各种性质。我们研究了(I)规范不变结构是否与光子态有关，以及(Ii)如何实现开弦边界条件，(4)研究了ADS_5×S^5上四维N=4超杨-米尔斯理论中的环方程和弦场方程之间的关系，认为四维N=4超杨-米尔斯理论和ADS_5×S^5时空中的超弦理论是等价的(ADS/CFT对应)。这项研究是向证明等价性迈出的一步，它表明，威尔逊回路所遵循的超杨-米尔斯理论中的回路方程可以被视为超弦场论的运动方程。虽然这一主题没有包含在最初的研究计划中，但我认为这是本项目下一阶段的重要内容。较少

The purpose of the present research project is to study the various non-perturbative aspects in sting theory using "string field theory", which is a formulation of string theory, and also to reconsider the formulation of string field theory itself. We carried out the following researches for the two kinds of string field theory, Cubic String Field Theory (CSFT) and Vacuum String Field Theory (VSFT):(1)Analysis of time-dependent solutions in CSFTCSF is a string field theory expanded around an unstable D-brane. We studied the behavior of time-dependent solutions which express the decay process of the D-brane. String field theory differs very much from ordinary field theories in that the former contains infinite derivatives with respect to the time-coordinate. Our analysis is important for understanding properties particular to string field theory.(2)Construction and analysis of time-dependent solutions in VSFTWe constructed and studied time-dependent solutions corresponding to the decay … More of an unstable D-brane in the framework of VSFT, which is a string field theory expanded around the configuration without D-branes. Via the analysis using, in particular, Monte Carlo simulations, we found that it is very likely that solutions with desirable profiles exist(3)Analysis of the various properties of VSFT around a D-brane classical solutionWe studied (i) whether the gauge invariance structure associated with the photon state, and (ii) how the open string boundary condition is realiezed, in VSFT expanded around the D-brane solution.(4)Study of the relation between the loop equation in 4-dimensional N=4 super Yang-Mills theory and string field equation on AdS_5×S^5Four-dimensional N=4 super Yang-Mills theory and superstring theory on AdS_5×S^5 space-time are believed to be equivalent to each other (AdS/CFT correspondence). This research is a step toward the proof of the equivalence by showing that the loop equation in super Yang-Mills theory obeyed by the Wilson loop can be regarded as the equation of motion of superstring field theory. Although this subject was not contained in the original research plan, I think this is an important next stage of the present project. Less