From Diffeomorphism to Dark Matter

从微分同胚到暗物质

• 批准号: 0244377
• 负责人: Vincent Rodgers
• 金额: $ 5万
• 依托单位: University of Iowa
• 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: 2003-06-15 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0244377&HistoricalAwards=false
• 关键词: Diffeomorphism; Dark; Matter

This proposal focuses on the study of coadjoint representations and related algebraic structures related to coadjoint orbits. These coadjoint representations play a fundamental role in understanding certain aspects of the Anti-de Sitter Space / conformal field theory conjecture as well as understanding such diverse topics as black hole quantization and conformal field theory. The research will focus on understanding the Virasaro algebra arising in string theory and its dual (the coadjoint representation). By considering the semi-direct product of the Virasoro algebra and the Kac-Moody algebra, two symplectic structures of classical mechanics can be obtained which are important for quantizing the theory. The resulting action can be used for describing quantization about BTZ black holes as well as for studying Chern Simons theory. A toy M theory will be studied based on a particular N=1 Virasaro action.

这项建议侧重于研究余伴表示和与余伴轨道相关的代数结构。这些共轭表示对于理解反德西特空间/共形场理论猜想的某些方面，以及理解诸如黑洞量子化和共形场理论等不同的主题起着基本的作用。这项研究将集中于理解弦理论中出现的Virasaro代数及其对偶(余伴表示)。通过考虑Virasoro代数和Kac-Moody代数的半直积，可以得到经典力学的两个辛结构，这两个辛结构对于量子化理论是重要的。所得作用量可用于描述BTZ黑洞的量子化，也可用于研究Chern Simons理论。玩具M理论将基于一个特殊的N=1 Virasaro作用量来研究。