Study of Non-Perturbative Dynamics of Superstring Theory through Supersymmetric Yang-Mills Theory

本研究项目的主要目的是了解超弦理论的非微扰性质，并通过分析超对称杨-米尔斯理论的各个方面给出其基本公式。关于非交换超杨-米尔斯理论孤子解的分析及其膜解释，我们已经取得了相当满意的结果，尽管在其他计划的课题中还有许多有待澄清的地方。然而，我们在利用弦场理论分析速子凝聚方面取得了显著的成果，这是原计划中没有包含的课题。以下是我们2000-2002年研究的具体描述：1)非交换超Yang-Mills理论单极子解的分析：我们在非交换参数θ的二阶下给出了非交换超Yang-Mills理论的单极子解，并给出了该解的膜解释。2)用弦场理论分析速子凝聚：我们证明了弦场理论的经典解表示具有速子凝聚的真空（速子真空），除了满足运动方程外，还满足BRST不变性的另一个重要要求。我们还对解周围的涨落进行了分析，得到的结果有力地支持了速子真空周围不存在物理开弦态的期望。3)真空弦场论的研究：我们对围绕速子真空展开的候选弦场论——真空弦场论（Vacuum String Field Theory， VSFT）是否与普通开放弦理论相关的问题进行了开创性的研究。我们构造了一个代表微扰真空的经典解，分析了解周围的涨落谱等，得到了支持期望的结果。

The main aim of the present research project has been to understand the non-perturbative properties of superstring theory and to give its basic formulation through the analysis of various aspects of supersymmetric Yang-Mills theory. We have obtained rather satisfactory results concerning the analysis of soliton solutions in non-commutative super Yang-Mills theory and its brane interpretation, though there still remains much to be clarified in other planned subjects. However, we have accomplished remarkable results in the analysis of tachyon condensation using String Field Theory, which is a subject not contained in the original plan. The following is a concrete description of our researches in the years 2000-2002:1) Analysis of monopole solution in non-commutative super Yang-Mills theory: We have presented, to second order in the non-commutativity parameter θ, the monopole solution to non-commutative super Yang-Mills theory, and given a brane interpretation to the solution.2) Analysis of tachyon condensation using string field theory: We have shown that the classical solution of string field theory representing the vacuum with tachyon condensation (tachyon vacuum) satisfies, besides the equation of motion, another important requirement of BRST invariance. We have also carried out an analysis of fluctuation around the solution to and obtained results which strongly support the expectation that there is no physical open string states around the tachyon vacuum.3) Study of Vacuum String Field Theory: We have carried out pioneering studies on the problem of whether Vacuum String Field Theory (VSFT), which is a candidate string field theory expanded around the tachyon vacuum, can be related to ordinary open string theory. We have constructed a classical solution representing the perturbative vacuum, analyzed the fluctuation spectra around the solution, and so on, and obtained results supporting the expectation.