CAREER: Effective Field Theories from String Compactification

该奖项资助北卡罗来纳大学教堂山分校乔纳森·赫克曼教授的研究活动。这项研究将集中于使用弦理论在最短的距离尺度上理解自然的工作原理。弦继续对理论物理产生重大影响，从亚原子粒子物理学到纯数学，都有跨学科的联系。最重要的悬而未决的问题之一是如何将这个框架与经过实验验证的亚原子粒子理论联系起来。这个项目的目的是使用弦理论预测的额外维度的几何来构建和研究与亚原子粒子理论和更正式的数学应用相关的理论模型。这个项目的教育和推广努力将向学生介绍几何方法在理论物理中的力量。1)在博士后和研究生阶段，PI将维持一个协作研究环境。2)PI将开设高能理论中的几何方法课程。3)在本科阶段，PI将通过他所在系举办的关于物理计算方法的北卡罗来纳大学REU计划，就弦理论的几何和计算方面向学生提供建议。4)PI将与莫尔黑德天文馆和科学中心密切合作，开发一套扩展模块，旨在传达高能理论家和实验者正在积极研究的广泛能量尺度。该计划的技术部分将专注于开发新的工具，研究强耦合下的弦紧凑，以及由此产生的低能量有效场理论。将特别强调F-理论的紧致化。这将需要发展相交七膜的世界体积理论中的开弦自由度和椭圆纤维Calabi-Yau流形捕获的闭弦自由度之间的对应关系。除了粒子物理和宇宙学的标准模型之外，更多的组件将需要为物理开发特定的弦驱动场景。粒子物理学的应用将包括研究具有强耦合额外扇区的动力学混合。宇宙学的应用将包括开发与混凝土细粒子物理模型相结合的充气再热场景。本项目还将重点使用F理论紧化的几何作为一种工具来分类和研究不同维度的超共形场理论(SCFT)。这将包括6D SCFT的分类，从奇异的Calabi-Yau四重几何的D3膜探针构造新的4D N=1 SCFT，以及通过在奇异的椭圆纤维Calabi-Yau五折叠上的紧致发展具有N=(0，2)超对称性的2D SCFT。

This award funds the research activities of Professor Jonathan Heckman at the University of North Carolina (UNC)at Chapel Hill. This research will focus on using string theory to understand the workings of Nature at the shortest distance scales. Strings continue to have significant impact on theoretical physics, with interdisciplinary connections ranging from the physics of subatomic particles to pure mathematics. One of the most important open issues is how to connect this framework to experimentally verified theories of subatomic particles. This project aims to use the geometry of extra dimensions predicted by string theory to construct and study theoretical models of relevance both for theories of subatomic particles, and for more formal mathematical applications.The education and outreach efforts of this program will introduce students to the power of geometric methods in theoretical physics. 1) At the postdoc and graduate level, the PI will maintain a collaborative research environment. 2) The PI will develop a course on geometric methods in high energy theory. 3) At the undergraduate level, the PI will advise students on geometric and computational aspects of string theory through the UNC REU program on computational methods in physics held in his department. 4) The PI will work closely with the Morehead Planetarium and Science Center to develop a set of outreach modules aimed at conveying the broad range of energy scales which are actively being investigated by high energy theorists and experimentalists.The technical components of this program will focus on the development of new tools in the study of string compactification at strong coupling, and the resulting low energy effective field theories. Particular emphasis will be placed on compactifications of F-theory. This will entail developing the correspondence between the open string degrees of freedom in the worldvolume theory of intersecting seven-branes, and closed string degrees of freedom captured by elliptically fibered Calabi-Yau manifolds. Additional components will entail the development of specific string-motivated scenarios for physics beyond the Standard Models of particle physics and cosmology. Particle physics applications will include the study of kinetic mixing with a strongly coupled extra sector. Cosmology applications will include the development of inflationary reheating scenarios coupled to concrete stringy particle physics models. This project will also focus on using the geometry of F-theory compactifications as a tool to classify and study superconformal field theories (SCFTs) in diverse dimensions. This will include a classification of 6D SCFTs, the construction of new 4D N = 1 SCFTs from D3-brane probes of singular Calabi-Yau fourfold geometries, and the development of 2D SCFTs with N = (0,2) supersymmetry from compactification on singular elliptically fibered Calabi-Yau fivefolds.