论文标题
超对称理论的扭曲指标的代数几何方法
An Algebro-Geometric Approach to Twisted Indices of Supersymmetric Gauge Theories
论文作者
论文摘要
本论文研究了三个维度的超对称阿伯仪理论的代数几何方面。证明超对称真空表现出Chern-Simons水平的窗口现象，该现象类似于量子K理论中带有水平结构的窗口现象。从半古典真空吸尘器，扭曲的手性环和扭曲的指标的角度研究了三维理论与量子K理论之间的对应关系。特别是，扭曲指数将代数几何解释作为有效量子力学的超对称指数。通过超对称定位，拓扑和涡旋鞍点的贡献均显示出与Jeffrey-Kirwan轮廓积分公式一致。 Chern-Simons对扭曲指数的代数几何结构从确定线束构成了与量子K理论的自然联系。
This thesis studies the algebro-geometric aspects of supersymmetric abelian gauge theories in three dimensions. The supersymmetric vacua are demonstrated to exhibit a window phenomenon in Chern-Simons levels, which is analogous to the window phenomenon in quantum K-theory with level structures. This correspondence between three-dimensional gauge theories and quantum K-theory is investigated from the perspectives of semi-classical vacua, twisted chiral rings, and twisted indices. In particular, the twisted index admits an algebro-geometric interpretation as the supersymmetric index of an effective quantum mechanics. Via supersymmetric localisation, the contributions from both topological and vortex saddle points are shown to agree with the Jeffrey-Kirwan contour integral formula. The algebro-geometric construction of Chern-Simons contributions to the twisted index from determinant line bundles provides a natural connection with quantum K-theory.
