权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Conforma Field Theory and Stringy Geometry

保形场论和弦几何

基本信息

批准号：
1914505
负责人：
Ilarion Melnikov
金额：
$ 13.26万
依托单位：
James Madison University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-15 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1914505&HistoricalAwards=false
关键词：
Conforma Field Theory Stringy Geometry

项目摘要

This award funds the research activities of Professor Ilarion V. Melnikov at James Madison University. Quantum Field Theory is a powerful mathematical framework that bears on almost every aspect of contemporary physics. These include the spectacularly successful Standard Model of Particle Interactions, the quantum phenomena in exotic materials that hold out great promise for new technologies such as quantum computing or energy storage and transfer, as well as theories that aim to uncover the fundamental laws of nature, such as String Theory. There has been tremendous progress in Quantum Field Theory over the past thirty years, and many questions that seemed intractable have been given precise and incisive answers. This project will build on those results by tackling a number of timely questions in Quantum Field Theory within realms where many of the standard tools are misleading or inapplicable. The project will also address questions in two-dimensional Quantum Field Theory, relevant both for the physics of exotic two-dimensional materials and for the emergent geometry of spacetime in String Theory. As a result, research in this area 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. Crucially, it will involve undergraduate researchers, who will be given a unique opportunity to engage in theoretical physics research and have early exposure to the mathematical and physical ideas at the forefront of current explorations. This research will also be interdisciplinary, bringing together collaborations of physicists and mathematicians, and it will be presented in public lectures to convey the exciting progress in and enthusiasm for research in theoretical physics. More technically, Professor Melnikov's work will explore foundational questions in conformal field theory and geometry in two-dimensional quantum field theory relevant to string compactification. In this setting powerful symmetries and constraints from spacetime geometry will help to give precise quantitative insights into strongly coupled quantum field theory and string propagation in non-trivial spacetimes. The project will address three concrete problems: (i) the characterization of obstructions to marginal deformations of supersymmetric conformal field theories and their relation to spacetime physics of the heterotic string; (ii) the identification of marginal deformations of conformal theories with local operators in asymptotically free gauge theories that reduce to the conformal theory in the low-energy limit; and (iii) the discovery of new conformal theories that enlarge the landscape of string vacua. It will bear on long-standing issues in stringy geometry and the mathematics and physics of (0,2) mirror symmetry --- a significant generalization of the mirror correspondence. The concrete lessons learned will also have wider applicability in low-dimensional quantum field theory at strong coupling.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.

该奖项资助詹姆斯麦迪逊大学教授Ilarion V. Melnikov的研究活动。量子场论是一个强大的数学框架，几乎涉及当代物理学的各个方面。这些包括非常成功的粒子相互作用标准模型，奇异材料中的量子现象，为量子计算或能量存储和转移等新技术带来了巨大的希望，以及旨在揭示自然基本定律的理论，如弦论。量子场论在过去的三十年里取得了巨大的进展，许多看似难以解决的问题都得到了精确而深刻的回答。该项目将建立在这些结果的基础上，在许多标准工具具有误导性或不适用的领域内解决量子场论中的一些及时问题。该项目还将解决二维量子场论中的问题，这些问题与奇异二维材料的物理学和弦论中时空的新兴几何学有关。因此，这一领域的研究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。该项目还将产生广泛的影响。至关重要的是，它将涉及本科研究人员，他们将获得一个独特的机会，从事理论物理研究，并在当前探索的最前沿早期接触数学和物理思想。这项研究也将是跨学科的，汇集了物理学家和数学家的合作，它将在公开讲座中提出，以传达理论物理研究的令人兴奋的进展和热情。从技术上讲，Melnikov教授的工作将探索与弦紧化相关的二维量子场论中的共形场论和几何学的基础问题。在这种情况下，时空几何的强对称性和约束将有助于对强耦合量子场论和非平凡时空中的弦传播给出精确的定量见解。该项目将解决三个具体问题：（i）表征超对称共形场论的边缘变形的障碍及其与杂化弦的时空物理学的关系;（ii）在低能极限下约化为共形理论的渐近自由规范理论中，用局部算子识别共形理论的边缘变形;和（iii）发现新的共形理论，扩大景观弦真空。它将涉及到弦几何和（0，2）镜像对称的数学和物理学中的长期问题-镜像对应的重要推广。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。