Research in Geometry, String Compactifications, and Mathematical String Theory

几何、弦紧化和数学弦理论研究

• 批准号: 1417410
• 负责人: Eric Sharpe
• 金额: $ 15万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2017-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1417410&HistoricalAwards=false
• 关键词: Research; Geometry; String; Compactifications; Mathematical

This award funds the research activities of Professor Eric Sharpe at Virginia Polytechnic Institute and State University. The goal of this project is to further develop technical tools and methods used to help extract real-world physics from string theory, the leading contender to unify general relativity with quantum field theory, two of the most significant developments of twentieth-century physics. The price one pays for that unification is a prediction that the world has more than four spacetime dimensions. One standard proposal to resolve that discrepancy is via a `compactification' of string theory, in which the extra dimensions are rolled up on some small compact space. It can be shown that the geometry and topology of that small compact space determine low-energy four-dimensional physics. This project will further develop tools and techniques for understanding compactifications of string theory and the predictions of various compactifications for low-energy four-dimensional physics.Technically, Professor Sharpe will study `gauged linear sigma models' (GLSM's), one of the most powerful tools used to study string compactifications. These tools have undergone a striking series of advances within the last few years. One part of that effort will revolve around extending the technology of supersymmetric localization in two-dimensional theories. As another part, Professor Sharpe will study dualities in nonabelian (2,2) and (0,2) supersymmetric gauge theories in two dimensions. Professor Sharpe will also continue developing quantum sheaf cohomology, a mathematical generalization of ordinary quantum cohomology that determines stringy nonperturbative corrections to charged matter couplings in heterotic string compactifications, with a special focus on understanding quantum sheaf cohomology in Grassmannians and other objects built via nonabelian GLSM's, as a stepping-stone to computing quantum sheaf cohomology in compact Calabi-Yau manifolds.

该奖项为弗吉尼亚理工学院和州立大学的Eric Sharpe教授的研究活动提供资金。 该项目的目标是进一步开发技术工具和方法，用于帮助从弦理论中提取现实世界的物理学，弦理论是统一广义相对论与量子场论的主要竞争者，这是20世纪物理学最重要的两个发展。 人们为这种统一所付出的代价是预言世界有多于四维的时空。 解决这个矛盾的一个标准建议是通过弦理论的“紧化”，其中额外的维度被卷起在一些小的紧凑空间中。 可以证明，这个小的紧致空间的几何和拓扑决定了低能四维物理。 这个项目将进一步发展工具和技术，以理解弦理论的紧化和各种低能量四维物理紧化的预测。在技术上，夏普教授将研究“规范线性西格玛模型”（GLSM），用于研究弦紧化的最强大的工具之一。 这些工具在过去几年中经历了一系列惊人的进步。 这项工作的一部分将围绕着在二维理论中扩展超对称定位技术。 作为另一部分，夏普教授将研究非阿贝尔（2，2）和（0，2）超对称规范理论在二维的对偶。 夏普教授还将继续开发量子层上同调，普通量子上同调的数学推广，确定杂合弦紧化中带电物质耦合的弦非微扰校正，特别关注理解Grassmannians和通过nonabelian GLSM构建的其他对象中的量子层上同调，作为计算紧凑的Calabi-Yau流形中量子层上同调的垫脚石。