D-Brane Physics and Calabi-Yau Geometry

D-膜物理和 Calabi-Yau 几何

• 批准号: 0301476
• 负责人: David Morrison
• 金额: $ 74.1万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-06-01 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0301476&HistoricalAwards=false
• 关键词: Brane; Physics; Calabi; Yau; Geometry

DMS-0301476David R. Morrison, Paul Aspinwall, and M. Ronen Plesser.String theory is one of the most challenging and interesting fields inboth mathematics and physics. Widely considered the most promisingapproach to formulating a complete unified model of physics at themost fundamental level, it has also spawned many ideas in puremathematics. The original idea of string theory was that all fundamental constituents of the universe were open or closed loops of string. It has become increasingly clear that this formulation of the theory is incomplete in essential ways. One of the missing pieces is the phenomenon known as "D-branes", which naively appear to be geometric objects of variousdimensions: points, strings, membranes, and so on, which coexist with the fundamental strings of the theory.A satisfactory mathematical framework for studying these D-branes, and an understanding of their physical nature, are lacking. In this project,mathematical techniques from algebra and geometry will be used to uncoverthe concepts required for a precise definition of these D-branes. Theresearchers will develop new mathematical tools, as needed, as well asapply existing mathematical tools to attack this problem. The physical nature of D-branes in non-trivial backgrounds will also be investigated in detail, using methods from quantum field theory and insights from supergravity. The insights gained from the study of D-branes will be applied back to the physics of gauge theory and string theory, as well.

david R. Morrison， Paul Aspinwall和M. Ronen Plesser。弦理论是数学和物理学中最具挑战性和最有趣的领域之一。它被广泛认为是在最基本的层面上形成完整统一的物理模型的最有希望的方法，它也在纯粹数学中产生了许多想法。弦理论最初的想法是，宇宙的所有基本成分都是弦的开环或闭环。越来越清楚的是，这一理论的表述在本质上是不完整的。缺失的部分之一是被称为“d膜”的现象，它天真地表现为各种维度的几何对象：点、弦、膜等等，它们与理论的基本弦共存。目前还缺乏一个令人满意的数学框架来研究这些d膜，以及对它们的物理性质的理解。在这个项目中，将使用代数和几何的数学技术来揭示精确定义这些d膜所需的概念。研究人员将根据需要开发新的数学工具，并应用现有的数学工具来解决这个问题。d膜在非平凡背景下的物理性质也将被详细研究，使用量子场论的方法和超重力的见解。从d膜的研究中获得的见解也将应用到规范理论和弦理论的物理学中。