Algebraic Geometry in String Theory

弦论中的代数几何

• 批准号: 1304962
• 负责人: Ron Donagi
• 金额: $ 33.7万
• 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: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1304962&HistoricalAwards=false
• 关键词: Algebraic; Geometry; String; Theory

This proposal explores some of the main research areas where algebraic geometry interacts with quantum field theory and string theory including: the moduli of super Riemann surfaces and the related issues of superstring measure and superstring perturbation theory; the geometric Langlands program; heterotic string phenomenology; F theory; and quantum sheaf cohomology. The proposal also considers some issues in moduli spaces of curves and abelian varieties, and some more exploratory math/physics connections such as amplitudes, Grassmannians, and twistors; and some conjectures regarding the 6-dimensional conformal field theory and its mathematical consequences.The significance of this project is in developing the connections between mathematics (mostly algebraic geometry) and high energy physics (mostly string theory). Each of these areas involves a mixture of issues from math and from physics, and most will be explored in teams involving both mathematicians and physicists. The first research area in particular is expected to have a major impact on the (mathematical) foundations of perturbative superstring theory, while the second addresses one of the major open problems in mathematics using new tools inspired, at least in part, by high energy physics ideas. The PI proposes also to continue a wide range of broad impact community and educational activities, including: the development and guidance of a series of conferences emphasizing the interactions of physics and mathematics, and of other channels for the dissemination of new knowledge concerning interactions of mathematics and high energy physics; curriculum development at the graduate and undergraduate level; writing a strings-for-mathematicians text; extensive work with graduate and undergraduate students and evaluation of the math major at Penn; membership of national bodies such as the AMS Committee on the Profession, and editorship of several journals and book series.This award is co-funded by DMS and PHY.

该提案探讨了代数几何形状与量子场理论和弦理论相互作用的一些主要研究领域，包括：超级黎曼表面的模量以及相关的SuperString Meses and SuperString扰动理论的相关问题；几何兰兰兹计划；杂弦现象学； F理论；和量子捆起来的共同体。该提案还考虑了曲线和阿贝尔品种的模量空间中的一些问题，以及一些更多的探索性数学/物理连接，例如振幅，格拉斯曼尼亚人和扭曲器；以及有关6维综合场理论及其数学后果的一些猜想。该项目的意义在于发展数学（主要是代数几何形状）和高能量物理学（主要是字符串理论）之间的联系。这些领域中的每个领域都涉及数学和物理学中的问题，大多数将在涉及数学家和物理学家的团队中进行探索。特别是第一个研究领域预计将对扰动超弦理论的（数学）基础产生重大影响，而第二个研究领域将使用高能量物理学的想法启发的新工具来解决数学中的主要开放问题之一。 PI还建议继续进行广泛的广泛影响社区和教育活动，包括：一系列会议的发展和指导，强调了物理学和数学的相互作用，以及其他渠道的相互作用，以传播有关数学和高能物理学相互作用的新知识；研究生和本科水平的课程发展；写一本书的弦乐器文字；与研究生和本科生的大量工作以及对宾夕法尼亚大学的数学专业的评估；国家机构的成员，例如AMS专业委员会，以及几个期刊和书籍系列的编辑。该奖项由DMS和PHY共同资助。