Studies of non-perturbative effects in supersymmetric theories by the localization method

我利用微扰/非微扰方法和超弦理论研究了规范理论中的各种问题，特别是规范理论具有超对称性。在我的研究项目中，我主要研究了以下6个主题：(1)三维chen - simons理论和二维BF理论的矩阵正则化和局域化(2)超对称规范理论和热带几何中的孤子(3)超弦理论中膜组态对自发超对称破缺的理解(4)利用重整化群流分析超对称规范理论中的对偶级联(5)规范场的新机制(6)用局部化方法评价BPS涡旋模空间的体积

I have studied various problems in gauge theory, which especially possesses the sypersymmetry, by using perturbative/non-perturbative methods and superstring theory. I have investigated mainly the following 6 themes in the period of my research project:(1) Matrix regularization of 3 dimensional Chern-Simons theory and 2 dimensional BF theory and Localization(2) Solitons in supersymmetric gauge theory and tropical geometry(3) Understanding of spontaneous supersymmetry breaking via brane configurations in superstring theory(4) Analysis of duality cascades in supersymmetric gauge theories by the renormalization group flow(5) Novel mechanism of the gauge field localization on the domain-walls(6) Evaluation of the volume of the moduli space of BPS vortices by the localization method