CAREER: Effective Field Theories from String Compactification

该奖项资助了北卡罗来纳大学教堂山分校的乔纳森·赫克曼教授的研究活动。这项研究将侧重于使用弦理论来理解自然在最短距离尺度上的运作。弦继续对理论物理产生重大影响，与从亚原子粒子物理学到纯数学的跨学科联系。最重要的开放问题之一是如何将这个框架与实验验证的亚原子粒子理论联系起来。该项目旨在利用弦理论预测的额外维度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。该计划的教育和推广工作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，项目负责人将保持合作研究的环境。2)学院将开设一门高能理论的几何方法课程。3)在本科阶段，PI将通过其所在系的UNC REU物理计算方法项目，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，开发一套外联模块，旨在传递高能理论家和实验家正在积极研究的大范围能量尺度。该计划的技术部分将侧重于开发新工具，研究强耦合下的弦紧化，以及由此产生的低能量有效场理论。特别强调的是f理论的紧化。这将需要发展七膜相交世界体积理论中的开弦自由度与椭圆纤维Calabi-Yau流形捕获的闭弦自由度之间的对应关系。额外的组件将需要在粒子物理和宇宙学的标准模型之外发展特定的弦驱动物理场景。粒子物理的应用将包括与强耦合额外扇区的动力学混合的研究。宇宙学的应用将包括与具体的弦粒子物理模型相结合的暴胀再加热场景的发展。本项目还将侧重于使用f理论紧化的几何作为工具来分类和研究不同维度的超共形场理论（SCFTs）。这将包括6D scft的分类，从奇异Calabi-Yau四重几何的d3膜探针构建新的4D N = 1 scft，以及从奇异椭圆纤维Calabi-Yau五重几何的紧化中发展N =(0,2)超对称的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.