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String Compactifications: From Geometry To Effective Field Theory

弦紧化：从几何到有效场论

基本信息

批准号：
1720321
负责人：
Lara Anderson
金额：
$ 60万
依托单位：
Virginia Polytechnic Institute and State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-15 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720321&HistoricalAwards=false
关键词：
String Compactifications Geometry Effective Field

项目摘要

This award funds the research activities of Professors Lara Anderson, James Gray, and Eric Sharpe at Virginia Tech.In string theory --- a proposal for a fundamental theory of quantum gravity --- the roles of physics and geometry are intrinsically intertwined. While the questions that string theory attempts to answer are physical, the path to those answers frequently leads to cutting-edge challenges in modern mathematics. This award will fund a collaborative program of research to explore the physics that arises from string compactifications. The goals of this work include strengthening the links between string theory and current progress in particle physics by developing new foundational tools for the subject of string phenomenology. In addition, Professors Anderson, Gray and Sharpe aim to further bound and characterize the geometries arising in string compactifications. Experience shows that when strong physical requirements are expressed in the language of geometry, they can open the door to new and unexpected results in both physics and mathematics. As a result, research in this area advances the national interest by promoting the progress of basic science. Professors Anderson, Gray and Sharpe will involve junior scientists in this project, including a postdoctoral researcher and several graduate students who will take part in the collaborative research. Their efforts will include the organizing of conferences and workshops that will increase dialog between physicists and mathematicians on pressing problems at the boundary of both fields. In all of these aspects of student training and professional dialog, Professors Anderson, Sharpe and Gray are committed to actively encouraging the inclusion of under-represented groups into the frontline of progress in the sciences. More specifically, the PIs will study two of the most flexible frameworks for four-dimensional compactifications of string theory: Heterotic string theory and F-theory. Within heterotic string theory, novel descriptions of the physical and geometric moduli spaces will be used to compute previously undetermined aspects of the effective theory, including the N=1 matter field Kahler potential and physically normalized Yukawa couplings. The nonperturbative contributions to Yukawa couplings will also be computed via quantum sheaf cohomology, a generalization of ordinary quantum cohomology. This work will explore new dualities including (0,2) mirror symmetry, as well as the global structure of the moduli space of SCFT's. Within F-theory, new results in the geometry of elliptic fibrations will be used to study the properties of singular Calabi-Yau manifolds and their links to Hitchin systems, as well as to study the implications of the ubiquity of multiply fibered manifolds for string dualities and effective theories. Recent progress in geometry will be used to extract new features of the effective theories describing F-theory compactifications, including the explicit four-dimensional field-dependent form of flux contributions to the superpotential.

该奖项资助弗吉尼亚理工大学的劳拉安德森、詹姆斯格雷和埃里克夏普教授的研究活动。在弦理论中-一个量子引力基本理论的建议-物理学和几何学的角色本质上是交织在一起的。虽然弦理论试图回答的问题是物理问题，但通往这些答案的道路经常导致现代数学的前沿挑战。该奖项将资助一项合作研究计划，以探索弦紧化产生的物理学。这项工作的目标包括加强弦理论和粒子物理学的当前进展之间的联系，通过开发弦现象学的新的基础工具。此外，安德森教授、格雷教授和夏普教授的目标是进一步限制和描述弦紧化中产生的几何形状。经验表明，当强烈的物理要求用几何语言表达时，它们可以为物理学和数学中的新的和意想不到的结果打开大门。因此，这一领域的研究通过促进基础科学的进步来促进国家利益。教授安德森，格雷和夏普将涉及初级科学家在这个项目中，包括博士后研究员和几个研究生谁将参加合作研究。他们的努力将包括组织会议和研讨会，以增加物理学家和数学家之间就两个领域边界上的紧迫问题进行对话。在学生培训和专业对话的所有这些方面，教授安德森，夏普和格雷致力于积极鼓励代表性不足的群体纳入科学进步的前沿。更具体地说，PI将研究弦理论的四维紧化的两个最灵活的框架：杂合弦理论和F理论。在杂化弦理论中，物理和几何模空间的新描述将被用来计算有效理论中以前未确定的方面，包括N=1物质场Kahler势和物理归一化的Yukawa耦合。非微扰对汤川耦合的贡献也将通过量子层上同调来计算，量子层上同调是普通量子上同调的推广。这项工作将探索新的对偶，包括（0，2）镜像对称，以及全球结构的模空间的SCFT的。在F理论中，椭圆纤维化几何的新结果将用于研究奇异卡-丘流形的性质及其与希钦系统的联系，以及研究多纤维流形的普遍存在对弦对偶和有效理论的影响。几何学的最新进展将被用来提取描述F理论紧致化的有效理论的新特征，包括对超势的通量贡献的明确的四维场依赖形式。