Holomorphic Vector Field and Topological Sigma Model on CP^1 World Sheet
Holomorphic Vector Field and Topological Sigma Model on CP^1 World Sheet
复制标题
CP^1 世界表上的全纯向量场和拓扑西格玛模型
DOI：
10.1142/s0217751x20501924
复制
发表时间：
2020
影响因子：
1.6
通讯作者：
Ken Kuwata
中科院分区：
文献类型：
--
作者：
Masao Jinzenji;Ken Kuwata
维滕提出，不动点定理可以由黎曼流形上的超对称sigma模型导出，其中势项是由一个Killing向量导出的.其中一个著名的不动点定理是Bott留数公式，它把Kähler流形上全纯向量丛的Chern类的交集数表示为全纯向量场的不动点集的贡献之和。本文利用描述从到的映射动力学的拓扑σ模型（A模型），引入由向量场导出的势项，导出了Bott剩余公式.我们的策略是将路径积分的相空间限制为同伦到常数映射的映射。由于在拓扑sigma模型中增加了一个势项，我们不得不修改原拓扑sigma模型的BRST对称性。我们的势项和BRST对称性与比斯利和Witten2在文章中所用的思想密切相关，其中考虑了由全纯向量丛的全纯截面诱导的势项和相应的超对称性.
Witten suggested that fixed-point theorems can be derived by the supersymmetric sigma model on a Riemann manifoldwith potential terms induced from a Killing vector on.3. One of the well-known fixed-point theorems is the Bott residue formula9which represents the intersection number of Chern classes of holomorphic vector bundles on a Kähler manifoldas the sum of contributions from fixed point sets of a holomorphic vector fieldon. In this paper, we derive the Bott residue formula by using the topological sigma model (A-model) that describes dynamics of maps fromto, with potential terms induced from the vector field. Our strategy is to restrict phase space of path integral to maps homotopic to constant maps. As an effect of adding a potential term to the topological sigma model, we are forced to modify the BRST symmetry of the original topological sigma model. Our potential term and BRST symmetry are closely related to the idea used in the paper by Beasley and Witten2where potential terms induced from holomorphic section of a holomorphic vector bundle and corresponding supersymmetry are considered.