From Diffeomorphism to Dark Matter

这个建议的重点是研究的余伴随表示和相关的代数结构相关的余伴随轨道。这些协伴随表示在理解Anti-de Sitter空间/共形场论猜想的某些方面以及理解黑洞量子化和共形场论等不同主题方面发挥着重要作用。研究将集中在理解弦理论中出现的Virasaro代数及其对偶（coadjoint表示）。 通过考虑Virasoro代数和Kac-Moody代数的半直积，得到了经典力学的两个辛结构，这对量子化理论有重要意义. 所得的作用量可以用来描述BTZ黑洞的量子化以及研究Chern Simons理论。一个玩具M理论将研究一个特殊的N=1 Virasaro行动的基础上。

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.