Comprehensive study on fundamental problems in string field theories

针对三维三次弦场论(CSFT)与Chern-Simons理论的数学结构的相似性，研究了CSFT的拓扑结构与其经典解之间的关系，并将其形式化为零的有限规范变换。特别地，我们发现KBC-代数(这是构造解的基本工具)中来自K=0的奇点以及来自K=∞特征值的奇点是解的缠绕数的来源。我们还给出了一种适当处理这些奇点的正则化方法。此外，我们还在交换K和1/K的变换下发现了一种新的对偶结构。利用这种对偶结构，我们提出了一种构造带有任意整数绕组数的解的方法。

Focusing on similarities between the mathematical structure of Cubic String Field Theory (CSFT) and that of the Chern-Simons theory in three dimensions, we studied the topological structure of CSFT in relation to its classical solutions which are given formally as finite gauge transforms of zero. We found, in particular, that the singularities from the K=0 as well as from the K=∞eigenvalues of the quantity K in the KBc-algebra (which is a basic tool for constructing solutions) are the origins of the winding number of the solutions. We also presented a regularization method for properly treating these singularities. In addition, we found a novel duality structure under a transformation which exchanges K and 1/K. By using this duality, we proposed a way of constructing solutions carrying arbitrary integer winding numbers.