String Phenomenology and Geometry

该奖项资助弗吉尼亚理工大学劳拉·B·安德森教授的研究活动。基本粒子物理学正处于发展的关键时刻。大型强子对撞机、普朗克卫星和其他实验的新研究将提供有关标准模型以外的可能物理的新信息。本项目正是在这一目标的推动下开展的。它的重点是弦理论，该理论希望将重力与其他基本力统一起来。弦理论只有在非常高的能量尺度下才能表现出来。为了与实验相联系，该项目专注于发展“弦现象学”--弦理论的一个方面，它试图弥合高能、超维的弦理论形式主义与低能量、四维的粒子和力世界之间的差距。尽管弦理论作为已知的唯一一致的引力量子理论很重要，而且它在高能物理中建立所谓的“自上而下”的模型方面具有巨大的能力和灵活性，但直到最近，弦理论的显式低能极限才开始发展到使弦和粒子现象学之间严肃的跨学科接触成为可能的水平。在弦理论中，物理和数学的作用本质上是相互交织的，弦现象学的进步需要现代数学中的尖端工具。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关联的方法。现在是时候尝试回答这个问题了：弦理论能描述真实世界吗？最后，通过跨学科的数学和物理方法以及不断扩大的计算能力，弦现象学能够做到这一点。通过探索这些新的几何结构，可能会发现弦理论的观点看起来与我们观察的世界极其相似。在杂种优势弦理论中，PI将生成一个包含数千亿个杂种模型(由Calabi-Yau 3折叠和在其上定义的矢量束组成)的数据库，以及完成几何分析和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化理论中长期存在的现象学挑战，例如模稳定性和确定完整的4维，N=1拉格朗日(包括卡勒势和归一化汤川耦合)。使用上面概述的相同的数学工具包，她还将研究全球F理论构造中的模型构建。尽管F理论是粒子现象学最有前途的严谨方法之一，但它并没有被完全理解。它的目标是通过系统地研究Calabi-Yau 4折叠的几何结构和其中7膜包裹的2维环(或洞)，为F理论模型的建立贡献一个严格的框架。此外，PI将通过在7膜堆上引入非阿贝尔规范场真空期望值(矢量束)来探索建模的新途径。最后，PI将研究以G2完整理论为背景的紧致奇异流形，还将研究G2完整(及其交集)7维空间中的特殊(奇点)点，并在这些奇点的邻域内导出M-理论紧化的显式4维有效场理论。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视角。

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.