Research in string compactifications and mathematical string theory

弦紧化和数学弦理论研究

• 批准号: 0755614
• 负责人: Eric Sharpe
• 金额: $ 9万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0755614&HistoricalAwards=false
• 关键词: Research; string; compactifications; mathematical; theory

The PI proposes to investigate the properties of four dimensional theories with N = 1 supersymmetry which are obtained from compactifications of string theory. Another topic of investigation will be the connection between geometry and string theory. Another objective will be to study a particular generalization of "mirror symmetry," a duality between typically topologically distinct spaces. The PI also hopes to study heterotic string compactifications with fluxes which involve understanding manifolds that are not of the usual Kahler variety. Other directions of this research include studying a class of string vacua derived from "hybrid" Landau-Ginzburg models.The broader impacts of this proposal are that the PI proposes a series of intensive two-week summer schools for visiting grad students and postdocs to teach relevant advanced mathematics to young physicists. This series of summer schools will help to fill what the PI perceives as a significant pedagogical gap in the training of young persons in this field namely the lack of schools to teach the advanced mathematics needed to make progress in formal string theory. The research advocated in this proposal is multidisciplinary in nature involving collaboration with mathematicians with expertise in geometry

PI提议研究具有n = 1超对称性的四个维理论的性质，这些理论是从弦理论的压缩中获得的。调查的另一个主题是几何和弦理论之间的联系。另一个目的是研究“镜像对称性”的特定概括，这是通常在拓扑不同的空间之间的二元性。 PI还希望使用通量研究杂种弦弦压缩，涉及了解不常见的Kahler品种的歧管。这项研究的其他方向包括研究源自“混合” Landau-Ginzburg模型的一类弦真空。该提案的更广泛影响是，PI提出了一系列为期两周的夏季学校，用于访问毕业生和博士后，以向年轻的物理学家教授相关的先进数学。这一系列的暑期学校将有助于填补PI认为是对该领域年轻人的培训的重要教学差距，即缺乏学校来教授正式弦乐理论取得进展所需的先进数学。该提议中主张的研究本质上是多学科的，涉及与具有几何学专业知识的数学家合作