Topics in String Theory and Quantum Field Theory

该奖项资助芝加哥大学教授杰弗里·A·哈维的研究活动。自然界中有四种已知的力：引力、电磁力和在核物理中起作用的弱力和强力。量子场论的框架为我们提供了除重力以外的所有力的数学描述，弦理论是一个有希望的、但未经实验检验的框架，可以将重力与其他自然力统一起来。量子场论和弦理论还没有完全被理解。解开它们结构的一种方法是专注于这些理论中约束它们结构的某些部分。这个项目将通过研究被称为“BPS态”的特殊状态的代数结构来揭示这些理论的新方法，并将研究这些理论的对称性的精确性质。这项研究通过增加我们对自然最基本层面的了解来促进国家利益-一种在过去最终导致在改进的技术和医学中的具体应用的理解。这项研究的更广泛影响包括培训博士后，他们将成为未来的科学领袖，并将在研讨会和公开演讲中介绍他们的研究。在更技术性的水平上，哈维教授将研究量子场论和弦理论中的BPS态代数及其对弱-强耦合二元性的影响。他还将评估弦理论中的对称是否总是规范对称，如果这被证明是正确的，他将研究如何构建协维-弦理论中的两个缺陷，这是规范对称的存在所隐含的。他的研究的其他方面将包括寻找特殊的或零星的有理保形场理论。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Jeffrey A. Harvey at the University of Chicago. There are four known forces in nature: the force of gravity, the electromagnetic force, and the weak and strong forces which play a role in nuclear physics. The framework of quantum field theory gives us a mathematical description of all the forces except for gravity, and string theory is a promising, but experimentally untested, framework for unifying gravity with the other forces of nature. Quantum field theories and string theories are not fully understood. One way to unravel their structure is to focus on certain parts of these theories which constrain their structure. This project will uncover new approaches to these theories by studying the algebraic structure of special states known as "BPS states" and will also study the precise nature of the symmetries of these theories. This research advances the national interest by increasing our understanding of nature at its most fundamental level --- an understanding that in the past has eventually led to concrete applications in improved technology and medicine. The broader impacts of this research include training for postdocs who will become future scientific leaders and will involve presentations of their research in seminars and public lectures.At a more technical level, Professor Harvey will study the algebra of BPS states in both quantum field theory and string theory and its consequences for weak-strong coupling duality. He will also assess whether symmetries in string theory are always gauge symmetries, and if this turns out to be correct, will study how one can construct the co-dimension-two defects in string theory which are implied by the existence of gauge symmetries. Other aspects of his research will include a search for exceptional or sporadic rational conformal field theories.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.