Mathematical Aspects of String Duality

弦对偶性的数学方面

• 批准号: 0405117
• 负责人: Kefeng Liu
• 金额: $ 11.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405117&HistoricalAwards=false
• 关键词: Mathematical; Aspects; String; Duality

AbstractAward: DMS-0405117Principal Investigator: Kefeng LiuBy using localization methods we plan to intensively studyvarious conjectures from string theory, in particular thosearised from string duality. These include the most general mirrorprinciple for higher genus from functorial localization, theGopakumar-Vafa integrality conjecture, the relationship betweenelliptic genus and Gromov-Witten invariants, both fromequivariant index theory. We have made significant progressestowards our goals, for which the functorial localization formulawe discovered during our proof of the mirror principle is one ofthe key techniques.The interactions of string theory and mathematics has been one ofthe very few most active and most exciting fields in mathematicsfor the past twenty years. String duality has created manyamazingly beautiful mathematical conjectures. Our localizationmethods have been very successful in proving them, inlcuding themirror conjecture, the Marino-Vafa conjecture, the Hori-Vafaconjecture and the mathematical construction of the topologicalvertex. Such interactions not only produce mathematical theoriesand results, but also give strong evidences to the physicaltheories.

AbstractAward：DMS-0405117首席研究员：刘科峰通过使用局部化方法，我们计划深入研究弦理论的各种结构，特别是弦对偶性。其中包括由函子局部化得到的最一般的高阶亏格镜像原理，Gopakumar-Vafa积分猜想，椭圆亏格与Gromov-Witten不变量之间的关系，这两个结果都是由等变指标理论得到的。我们已经朝着我们的目标取得了重大的进展，其中在镜像原理的证明过程中发现的函子定域公式是其中的关键技术之一，弦理论与数学的相互作用是近二十年来物理学中为数不多的最活跃、最令人兴奋的领域之一。 弦对偶性创造了许多令人惊奇的美丽数学图形。我们的局部化方法在证明它们方面是非常成功的，包括镜像猜想、Marino-Vafa猜想、Hori-Vafa猜想和拓扑顶点的数学构造。这种相互作用不仅产生了数学理论和结果，而且为物理理论提供了有力的证据。