Algebraic Geometry and Quantum Field Theory of D-Branes

D-膜的代数几何和量子场论

• 批准号: 0606578
• 负责人: Paul Aspinwall
• 金额: --
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0606578&HistoricalAwards=false
• 关键词: Algebraic; Geometry; Quantum; Field; Theory

AbstractAward: DMS-0606578Principal Investigator: David R. Morrison, Paul S. Aspinwall, M. Ronen PlesserA D-brane, roughly, is something on which an open string may end.Any detailed exploration of this notion quickly reveals that therough notion is too crude, and that all of the subtleties of thegeometry of string theory come into play in full force indescribing D-branes. The proposers will investigate both themathematical and physical properties of D-branes, drawing upontechniques from algebraic geometry (particularly complexthreefolds), homological algebra, and derived categories on themathematics side, and on quantum field theory and supergravityfrom the physics side. The proposers anticipate that the studyof the complementary mathematical and physical aspects of thisstory will shed light on each other, and that new results in bothpure mathematics and theoretical physics will be obtained as aconsequence.This study is part of a broader exploration of the mathematicalaspects of an important current theme in theoretical physics:modeling the particles and forces of nature using one-dimensionalobjects ("strings") instead of the traditional zero-dimensionalobjects ("points"). Physical models of this kind arequantum-mechanical in nature but also model the gravitationalforce, thus reconciling one of the great puzzles in theoreticalphysics (namely, the apparent incompatibility of quantummechanics and Einstein's theory of gravity). One of theimportant discoveries of the past decade is that strings may haveendpoints which are constrained to lie in particular directions.The places where the endpoints of strings "attach" are known asD-branes, and these will be the subject of detailed mathematicalstudy in the current project.

摘要奖：DMS-0606578主要研究员：David R. Morrison、Paul S. Aspinwall、M. Ronen Plesser 粗略地说，D 膜是一个开放弦可能结束的东西。对这个概念的任何详细探索很快就会发现，粗略的概念过于粗糙，弦理论几何的所有微妙之处在描述 D 膜时都充分发挥作用。 提议者将研究 D 膜的数学和物理性质，在数学方面利用代数几何（特别是复数三重）、同调代数和派生范畴的技术，在物理方面利用量子场论和超引力。 提议者预计，对这个故事互补的数学和物理方面的研究将相互阐明，并且最终将获得纯数学和理论物理方面的新结果。这项研究是对理论物理中当前重要主题的数学方面进行更广泛探索的一部分：使用一维物体（“弦”）而不是使用一维物体（“弦”）对自然的粒子和力进行建模 传统的零维对象（“点”）。 这种物理模型本质上是量子力学的，但也模拟了引力，从而解决了理论物理学中的一大难题（即量子力学和爱因斯坦引力理论的明显不相容）。 过去十年的重要发现之一是弦可能有被限制在特定方向的端点。弦端点“附着”的地方被称为D-膜，这些将成为当前项目中详细数学研究的主题。