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。 该项目的目的是进一步开发用于帮助从字符串理论中提取现实世界物理学的技术工具和方法，这是统一与量子场理论一般相对论的主要竞争者，这是20世纪物理学的两个最重要的发展。 一个统一的价格是一个超过四个时空维度的预测。 解决该差异的一个标准建议是通过弦理论的“紧凑”来解决，其中额外的维度在一些小的紧凑空间上卷起。 可以表明，小紧凑空间的几何形状和拓扑决定了低能四维物理。 该项目将进一步开发工具和技术，以理解弦理论的压缩以及对低能量四维物理学的各种压缩的预测。技术上，夏普教授将研究“测量线性Sigma模型”（GLSM），这是用于研究字符串压缩的最强大工具之一。 在过去的几年中，这些工具在过去几年中都经历了一系列引人注目的进步。 这项工作的一部分将围绕扩展二维理论中超对称定位的技术。 作为另一部分，夏普教授将研究二维的非亚伯（2,2）和（0,2）超对称仪的二元性。 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卡拉比远流动。