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.

该奖项资助弗吉尼亚理工学院暨州立大学埃里克·夏普教授的研究活动。 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，弦理论是将广义相对论与量子场论（二十世纪物理学最重要的两个发展）统一起来的主要竞争者。 人们为这种统一所付出的代价是预测世界有四个以上的时空维度。 解决这一差异的一个标准建议是通过弦理论的“紧凑化”，其中额外的维度被卷入一些小的紧凑空间上。 可以证明，小致密空间的几何形状和拓扑结构决定了低能四维物理。 该项目将进一步开发工具和技术，用于理解弦理论的紧化以及低能四维物理的各种紧化的预测。从技术上讲，夏普教授将研究“测量线性西格玛模型”（GLSM），这是最强大的模型之一用于研究字符串压缩的工具。 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扩展二维理论中的超对称局域化技术。 作为另一部分，夏普教授将研究二维非阿贝尔 (2,2) 和 (0,2) 超对称规范理论的对偶性。 Sharpe 教授还将继续开发量子束上同调，这是普通量子上同调的数学概括，用于确定异质弦紧化中带电物质耦合的弦非微扰校正，特别关注理解格拉斯曼量和通过非阿贝尔 GLSM 构建的其他物体中的量子束上同调，作为计算紧凑卡拉比-丘流形中的量子束上同调的垫脚石。