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与量子场论和弦理论相互作用的一些主要研究领域，包括：超黎曼曲面的模以及超弦测度和超弦微扰理论的相关问题；几何朗兰兹纲领；杂种优势弦现象学； F理论；和量子束上同调。该提案还考虑了曲线模空间和阿贝尔簇中的一些问题，以及一些更具探索性的数学/物理联系，例如振幅、格拉斯曼量和扭量；以及关于6维共形场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）和高能物理（主要是弦理论）之间的联系。这些领域中的每一个都涉及数学和物理学问题的混合，并且大多数将由数学家和物理学家组成的团队进行探索。特别是第一个研究领域预计将对微扰超弦理论的（数学）基础产生重大影响，而第二个研究领域则使用至少部分受高能物理启发的新工具解决数学中的一个主要开放问题想法。 PI还建议继续开展广泛影响的社区和教育活动，包括：开发和指导一系列强调物理和数学相互作用的会议，以及传播有关数学相互作用的新知识的其他渠道和高能物理；研究生和本科生课程开发；为数学家编写字符串文本；与研究生和本科生进行广泛的合作，并对宾夕法尼亚大学数学专业进行评估； AMS 专业委员会等国家机构的成员，以及多种期刊和丛书的编辑。该奖项由 DMS 和 PHY 共同资助。