String Compactifications: From Geometry to Effective Field Theory

弦紧化：从几何到有效场论

• 批准号: 2310588
• 负责人: Lara Anderson
• 金额: $ 83.44万
• 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: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2310588&HistoricalAwards=false
• 关键词: String; Compactifications; Geometry; Effective; Field

This award funds the research activities of Professors Lara Anderson, James Gray, and Eric Sharpe at Virginia Tech.String theory is a proposal for a fundamental theory of how nature operates in which 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 involves cutting-edge challenges in modern mathematics. This award funds a collaborative program of research to explore the physics that arises from string theory. Because string theory predicts extra unseen dimensions beyond length, width, and height, these extra dimensions must be "curled up" in ways that render them too small to be detected with current experiments. However, the physics that string theory predicts depends crucially on the geometric properties of these curled-up dimensions. The goals of this work include strengthening the links between string theory and current progress in particle physics, in part by bounding and characterizing the geometries associated with these curled-up dimensions. 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 providing new insights into fundamental physics. Professors Anderson, Gray and Sharpe will also involve junior scientists in this project, including a postdoctoral researcher and several graduate students. Their efforts will include the organizing of conferences and workshops that will increase dialog between physicists and mathematicians on pressing problems at the boundary between both fields. In all of these aspects of student training and professional dialog, Professors Anderson, Gray and Sharpe are committed to actively encouraging the inclusion of members of under-represented groups into the frontline of progress in the sciences.More specifically, Professors Anderson, Gray, and Sharpe will investigate a new class of symmetries (known as higher-form symmetries), and two of the most flexible frameworks for four-dimensional compactifications of string theory, namely heterotic string theory and F-theory. They will also investigate a striking application known as decomposition. This is an observation that quantum field theories with certain higher-form symmetries are equivalent to disjoint unions of other quantum field theories. Within heterotic string theory, novel geometric tools 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 (including non-perturbative contributions). The goal of this study will be to understand the masses and interactions of particles within string compactification. Furthermore, new tools will be developed to study the physics of topology-changing transitions within heterotic string theory. In the context of F-theory, new results in the geometry of elliptic fibrations will be used to study the possible boundedness of the set of smooth Calabi-Yau varieties, heterotic/F-theory duality and the explicit four-dimensional field dependent form of flux contributions to the superpotential. Finally, Professors Anderson, Gray and Sharpe will also apply some of their recent insights into the global structure of moduli spaces of SCFTs to study possible swampland conjectures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项资助弗吉尼亚理工大学劳拉·安德森（Lara Anderson）、詹姆斯·格雷（James Gray）和埃里克·夏普（Eric Sharpe）教授的研究活动。弦理论是关于自然如何运作的基本理论的提议，其中物理和几何的作用本质上是相互交织的。 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涉及现代数学的前沿挑战。 该奖项资助一项合作研究计划，以探索弦理论产生的物理学。 由于弦理论预测了超出长度、宽度和高度之外的额外的看不见的维度，因此这些额外的维度必须以某种方式“卷曲”，使它们太小而无法通过当前的实验检测到。 然而，弦理论所预测的物理学在很大程度上取决于这些卷曲维度的几何特性。 这项工作的目标包括加强弦理论与粒子物理学当前进展之间的联系，部分方法是通过限制和表征与这些卷曲维度相关的几何形状。经验表明，当用几何语言表达强烈的物理要求时，它们可以为物理和数学方面新的、意想不到的结果打开大门。因此，该领域的研究通过提供对基础物理学的新见解来促进国家利益。 安德森、格雷和夏普教授还将让年轻科学家参与该项目，其中包括一名博士后研究员和几名研究生。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关于两个领域边界的紧迫问题的对话。在学生培训和专业对话的所有这些方面，安德森、格雷和夏普教授致力于积极鼓励代表性不足的群体成员纳入科学进步的前线。更具体地说，安德森、格雷和夏普教授夏普将研究一类新的对称性（称为更高形式的对称性），以及弦理论四维紧化的两个最灵活的框架，即异质弦理论和 F 理论。他们还将研究一种称为分解的引人注目的应用。 这是一个观察结果，即具有某些更高形式对称性的量子场论等效于其他量子场论的不相交并。在异质弦理论中，新颖的几何工具将用于计算有效理论先前未确定的方面，包括 N=1 物质场卡勒势和物理归一化汤川耦合（包括非微扰贡献）。 这项研究的目标是了解弦紧化过程中粒子的质量和相互作用。此外，还将开发新的工具来研究杂优势弦理论中拓扑变化转变的物理原理。在 F 理论的背景下，椭圆纤维振动几何的新结果将用于研究光滑 Calabi-Yau 簇集的可能有界性、杂种/F 理论对偶性以及显式四维场依赖形式通量对超势的贡献。最后，Anderson、Gray 和 Sharpe 教授还将应用他们最近对 SCFT 模空间全局结构的一些见解来研究可能的沼泽地猜想。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力评估进行评估，认为值得支持。优点和更广泛的影响审查标准。