Research Project in Algebraic Geometry and String Theory

代数几何和弦理论研究项目

• 批准号: 0612992
• 负责人: Ron Donagi
• 金额: $ 28.46万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0612992&HistoricalAwards=false
• 关键词: Research; Project; Algebraic; Geometry; String

The recent breakthrough in producing the Standard Model of particlephysics within heterotic string theory is a perfect illustration of thepower of algebraic geometry at the service of physics. Using techniquesfor construction of non simply connected Calabi-Yau threefolds and ofbundles on them satisfying various constraints on their chern classes andcohomology, the PI and a collaborator have recently constructed the onlyknown example of a heterotic string compactification which producesexactly the Minimal Suppersymmetric Standard Model (MSSM) spectrum ofparticles and forces, with no unwanted exotic matter. This opens upnumerous questions related to investigation of the High Country region ofthe Landscape of string vacua. These problems are of great interest inboth algebraic geometry and string phenomenology. Other physics questionsinvestigated in this proposal using techniques of algebraic geometryinclude exploration of the duality between the heterotic string andF-theory, and the Large N Duality. The purely geometric issues includeseveral extensions of the spectral construction and Fourier- Mukaitransforms to gerbes and non-commutative and related situations where suchextensions would have many applications. These yield a proof of Langlandsduality for Hitchin systems with arbitrary structure groups, and includeseveral problems about the moduli of Calabi-Yaus, their degenerations, andthe integrable systems arising from them.String theory is the leading physical candidate for a unified fieldtheory, incorporating both general relativity and quantum field theory.Algebraic geometry is the mathematical investigation of spaces defined byalgebraic equations. It provides an extermely versatile and powerful toolfor applications to string theory and to many other areas. The main thrustof this proposal is the use of techniques from algebraic geometry toderive the Standard Model of particle physics as a concrete instance ofstring theory.

最近在杂化弦理论中产生粒子物理标准模型的突破是代数几何为物理服务的力量的完美例证。利用构造非单连通的Calabi-Yau三折叠和满足其chern类和上同调的各种约束的丛的技术，PI和一个合作者最近构造了唯一已知的杂合弦紧化的例子，该例子精确地产生了粒子和力的最小超对称标准模型（MSSM）谱，没有不必要的奇异物质。这就引出了许多与调查弦真空景观的高地地区有关的问题。这些问题在代数几何学和弦现象学中都有着重要的意义。其他物理问题的调查，在这个建议使用技巧的代数geometryincluding探索的对偶性之间的杂弦和F-理论，和大N对偶。纯几何问题包括谱结构的几个扩展和Fourier-Mukaittransforms到gerbes和非交换和相关的情况下，这样的扩展将有许多应用。这些结果证明了具有任意结构群的希钦系统的Langlandsduality，并包括了关于Calabi-Yaus模的几个问题，它们的退化，以及由此产生的可积系统。弦理论是统一场论的主要物理候选者，结合了广义相对论和量子场论。代数几何是对由代数方程定义的空间的数学研究。它为弦理论和许多其他领域的应用提供了一个极其通用和强大的工具。这一建议的主旨是使用代数几何的技巧来推导粒子物理学的标准模型，作为弦理论的一个具体实例。