Research in Elementary Particle Physics

该奖项资助了芝加哥大学杰弗里·哈维教授的研究活动。随着人们寻找已久的希格斯玻色子最近的发现，粒子物理学的理论框架（所谓的粒子物理学的“标准模型”）现在已经完成了。然而，关于物质和能量的基本结构及其相互作用，仍有许多重要的悬而未决的问题。这些问题包括需要什么样的数学结构来结合引力和量子力学，以及暗物质和暗能量的起源。弦理论为解决这些问题提供了一个可能的框架。哈维教授将进行两条独立的研究路线，以解决这些问题。这个项目的第一部分涉及到“小弦理论”的研究——这个理论有一些与弦理论相同的优点，但更容易分析。该项目的第二部分涉及纯数学领域的研究，该领域与弦理论产生的技术密切相关。因此，该项目通过促进科学在其最基本的方向之一的进步来促进国家利益：发现和理解新的物理定律。该项目还将产生更广泛的重大影响。这项研究将涉及博士后、研究生，有时甚至包括本科生，从而在下一代物理学家开始研究时为他们提供关键的培训。PI还将在国际学校和研讨会上演讲，并参加芝加哥地区的公共宣传活动。从技术上讲，PI将扩展最近在小弦理论中计算BPS状态的工作，以研究N=2超对称的更一般背景。他还将继续研究非紧共形场论及其与模拟模形式的联系。这项工作对超对称场论中BPS态的研究以及各种物理有趣环境下弦理论的研究具有重要意义。该项目的第三个组成部分涉及零星组和各种类型的模块化和模拟模块化形式之间一些仍然神秘的联系的数学。特别是，他将通过扩展顶点算子代数的技术来扩展目前正在进行的工作。

This award funds the research activities of Professor Jeffrey Harvey at the University of Chicago.With the recent discovery of the long-sought Higgs boson, the theoretical framework underlying particle physics (the so-called "Standard Model" of particle physics) is now complete. However, there are still many important outstanding questions involving the fundamental structure of matter and energy and their interactions. These include what sorts of mathematical structures are needed to combine gravity and quantum mechanics, as well as the origin of dark matter and dark energy. String theory provides one possible framework to address these questions. Professor Harvey will pursue two independent lines of research aimed at addressing these questions. The first part of this project involves the study of "Little String Theory" - a theory that has some of the same good features of string theory but is easier to analyze. The second part of this project involves research in an area of pure mathematics that has close ties to techniques that grew out of string theory. This project thus advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical laws. This project will also have significant broader impacts. The research will involve postdocs, graduate students and even at times undergraduate students, thus providing critical training for the next generation of physicists as they start research. The PI will also lecture at international schools and workshops and also participate in public outreach events in the Chicago area.More technically, the PI will extend recent work on counting BPS states in Little String Theory to the study of more general backgrounds with N=2 supersymmetry. He will also continue his study of non-compact Conformal Field Theories and their connection to mock modular forms. This work has implications for the study of BPS states in supersymmetric field theories and to the study of string theory in a variety of physically interesting settings. A third component of this project involves the mathematics of some still-mysterious connections between sporadic groups and various types of modular and mock modular forms. In particular he will extend work currently in progress by extending techniques of Vertex Operator Algebras.