The Algebraic Structure of Topological Field Theory

拓扑场论的代数结构

• 批准号: 9704320
• 负责人: Ezra Getzler
• 金额: $ 11.2万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704320&HistoricalAwards=false
• 关键词: Algebraic; Structure; Topological; Field; Theory

9704320 Getzler In this project the investigator is to clarify the algebraic structures underlying certain recent discoveries in theoretical physics including the two-dimensional topological sigma model, topological gravity, and Gromov-Witten invariants. In particular, a structure theory for Gromov-Witten invariants is to be derived, and Gromov-Witten invariants of higher genus are to be computed. In mathematical terms, these invariants relate to various enumerative questions in algebraic geometry. For example, Gromov-Witten invariants of genus zero appear in the so called mirror symmetry phenomenon. Gromov-Witten invariants originally arose in theoretical physics - they describe a coupling of topological gravity with a model of conformal field theory. They play an important role in the popular 10-dimensional string model of the universe. The string theory model contains six hidden dimensions which form a tightly curved space known as Calabi-Yau manifold; Gromov-Witten invariants can be used to study various mathematical properties of Calabi-Yau manifolds.

9704320盖茨勒在这个项目中，研究人员将阐明理论物理中某些最新发现背后的代数结构，包括二维拓扑西格玛模型、拓扑引力和格罗莫夫-维腾不变量。特别地，推导了Gromov-Witten不变量的结构理论，并计算了高亏格的Gromov-Witten不变量。在数学术语中，这些不变量与代数几何中的各种计数问题有关。例如，零亏格的Gromov-Witten不变量出现在所谓的镜像对称现象中。Gromov-Witten不变量最初出现在理论物理中--它们描述了拓扑引力与保形场理论模型的耦合。它们在流行的宇宙10维弦模型中扮演着重要的角色。弦理论模型包含六个隐藏维度，它们形成了一个称为Calabi-Yau流形的紧曲空间；Gromov-Witten不变量可用于研究Calabi-Yau流形的各种数学性质。