Focused Research Group: Calabi-Yau Manifolds and their Applications

摘要：奖项：dms -0074072首席研究员：David R. morrison该研究项目汇集了来自三个校区的数学家和物理学家团队，共同研究弦理论。具体的研究任务包括研究八增压理论中超多重模空间的量子修正，异质弦紧化模空间的结构，全局完整群位于例外李群G2的七维空间中紧化场的m理论模型，calabi - yaufourfold上的m理论模型，以及膜奇点的AdS/CFT对应关系的研究。在最基本的层面上，弦理论很有希望成为宇宙统一理论的候选者。虽然基本思想很简单——基本粒子应该被建模为弦的数学循环而不是点——但这个理论的细节涉及并激发了一些复杂的数学工具和思想。即使在数学和物理协同作用特别富有成效的领域，对经典弦运动方程解的Calabi-Yau空间的研究，任务也不是完成的。这是一个由杜克大学、哥伦比亚大学和罗格斯大学的数学家和物理学家组成的研究小组获得的三个相关奖项之一。该奖项的资金为杜克大学的研究人员提供核心支持，并通过视频会议和旅行支持这个跨学科小组的合作。

AbstractAward: DMS-0074072Principal Investigator: David R. MorrisonThis research project brings together a team of mathematiciansand physicists based at three campuses to work together on stringtheory. Specific research tasks include the study of the quantumcorrections to the mypermultiplet moduli spaces in theories witheight supercharges, the structure of the moduli spaces ofheterotic string compactifications, M-theory models compactifiedon seven-dimensional spaces whose global holonomy group lies inthe exceptional Lie group G2, M-theory models on Calabi-Yaufourfolds, and a study of the AdS/CFT correspondence for branesat singularities.String theory is a promising candidate for a unifying theory ofthe universe at its most fundamental levels. Although the basicidea is simple - elementary particles should be modeled asmathematical loops of stgring rather than as points - working outthe details of this theory has involved and inspired somesophisticated mathematical tools and ideas. The task is by nomeans complete, even in an area where the synergy betweenmathematics and physics has been particularly productive, thestudy of the Calabi-Yau spaces that appear as solutions of theclassical string equations of motion. This is one of threelinked awards to a research group that includes mathematiciansand physicists at Duke University, Columbia University, andRutgers University. Funds in this award provide core support forthe researchers at Duke and are supporting this interdisciplinarygroup's collaborations through videoconferencing and travel.