String Phenomenology and Geometry

弦现象学与几何

• 批准号: 1417337
• 负责人: Lara Anderson
• 金额: $ 9.5万
• 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: 2014
• 资助国家: 美国
• 起止时间: 2014-07-15 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1417337&HistoricalAwards=false
• 关键词: String; Phenomenology; Geometry

This award funds the research activities of Professor Lara B. Anderson at Virginia Tech. Fundamental particle physics is at a critical moment in its development. New studies at the Large Hadron Collider, the Planck satellite and other experiments will give new information on possible physics beyond the Standard Model. This project is motivated by this goal. It is focused on string theory, which hopes to unify gravity with the other fundamental forces. String theory is only manifest at very high energy scales. To connect with experiment, the project concentrates on the development of "string phenomenology" - the aspect of string theory that attempts to bridge the gap between the high-energy, extra-dimensional formalism of string theory, and the low-energy, four-dimensional world of particles and forces. Despite the importance of string theory as the only known consistent quantum theory of gravity and its enormous power and flexibility for so-called "top down" model building in high energy physics, it is only recently that explicit low-energy limits of string theory have started to be developed to a level that makes serious interdisciplinary contact between string and particle phenomenology possible. Within string theory, the roles of physics and mathematics are intrinsically intertwined, and progress in string phenomenology requires cutting edge tools in modern mathematics. This project involves three of the primary approaches to particle phenomenology in string theory and interlinked approaches to string theory, algebraic geometry and high-speed mathematical computing. Now is the time to attempt to answer the question: can string theory give a description of the real world? And at last, with interdisciplinary mathematical and physical approaches and expanding computational power, string phenomenology is capable of doing just that. By exploring these new geometries, it may be possible to find a view of string theory that looks profoundly similar to the world we observe. In heterotic string theory, the PI will generate a database of hundreds of billions of heterotic models (composed of Calabi-Yau 3-folds and vector bundles defined over them) and the analytic and algorithmic tools necessary to completely analyze the geometries and compute their local and topological data. The PI will also use new approaches in computational algebraic geometry to address long-standing phenomenological challenges in heterotic theory such as moduli stabilization and the determination of the full 4-dimensional, N=1 lagrangian (including the Kahler potential and normalized Yukawa couplings). Using the same mathematical toolkit outlined above, she will also study model building within global F-theory constructions. Despite being one of the most promising stringy approaches to particle phenomenology, F-theory is not fully understood. It is the goal to contribute to a rigorous framework for F-theory model building by systematically studying the geometry of Calabi-Yau 4-folds and the 2-dimensional cycles (or holes) within them that 7-branes wrap. In addition, the PI will explore new avenues of model building by introducing non-Abelian gauge field vacuum expectation values (vector bundles) over 7-brane stacks. Finally, the PI will study compact singular manifolds with G2 holonomy as backgrounds for M-theory and will also investigate the special (singular) points in 7-dimensional spaces of G2 holonomy (and their intersections), and derive the explicit 4-dimensional effective field theory of a compactification of M-theory in the neighborhood of these singularities. The PI hopes for the first time to produce globally defined G2 compactifications of M-theory. A combination of these three approaches should yield a new view of string phenomenology in string theory.

该奖项为Lara B教授的研究活动提供资金。弗吉尼亚理工大学的安德森。基本粒子物理学正处于其发展的关键时刻。大型强子对撞机、普朗克卫星和其他实验的新研究将为标准模型之外的可能物理学提供新的信息。 这个项目就是由这个目标推动的。 它专注于弦理论，希望将引力与其他基本力统一起来。 弦理论只在非常高的能量尺度下才显现出来。 为了与实验相联系，该项目集中于“弦现象学”的发展--弦理论的一个方面，试图弥合弦理论的高能、超维形式与低能、四维粒子和力世界之间的差距。尽管弦理论作为唯一已知的一致的引力量子理论的重要性，以及它在高能物理学中所谓的“自上而下”模型构建中的巨大力量和灵活性，但直到最近，弦理论的明确低能极限才开始发展到一个水平，使弦和粒子现象学之间的跨学科联系成为可能。在弦理论中，物理学和数学的角色本质上是交织在一起的，弦现象学的进步需要现代数学的尖端工具。这个项目涉及弦理论中粒子现象学的三种主要方法，以及弦理论、代数几何和高速数学计算的相互联系的方法。 现在是尝试回答这个问题的时候了：弦理论能描述真实的世界吗？最后，随着跨学科的数学和物理方法以及不断扩展的计算能力，弦现象学有能力做到这一点。通过探索这些新的几何，我们或许可以找到一种与我们所观察到的世界极为相似的弦理论观点。在杂种优势弦理论中，PI将生成一个包含数千亿个杂种优势模型的数据库（由Calabi-Yau 3-folds和定义在其上的向量束组成）以及完整分析几何形状并计算其局部和拓扑数据所需的分析和算法工具。PI还将使用计算代数几何中的新方法来解决杂种优势理论中长期存在的现象学挑战，例如模量稳定和确定完整的4维N=1拉格朗日量（包括Kahler势和归一化Yukawa耦合）。使用上述相同的数学工具包，她还将研究全球F理论结构中的模型构建。尽管F理论是粒子现象学最有前途的弦方法之一，但它并没有被完全理解。我们的目标是通过系统地研究卡-丘4-折叠的几何结构和7-膜包裹的2维循环（或洞），为F-理论模型的建立提供一个严格的框架。此外，PI将通过引入7膜堆上的非阿贝尔规范场真空期望值（矢量束）来探索模型构建的新途径。最后，PI将研究以G2完整性为背景的紧致奇异流形，并将研究G2完整性的7维空间中的特殊（奇异）点（及其交点），并在这些奇点附近导出M理论紧致化的显式4维有效场论。PI希望第一次产生M理论的全局定义的G2紧化。 这三种方法的结合应该会产生弦理论中弦现象学的新观点。