From Diffeomorphism to Dark Matter

本文主要研究伴随轨道的伴随表示和相关代数结构。这些协表示在理解反德西特空间/共形场论猜想的某些方面以及理解诸如黑洞量子化和共形场论等各种主题方面发挥着基本作用。研究的重点是理解弦理论中出现的Virasaro代数及其对偶（协表示）。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，这对理论的量子化具有重要意义。由此产生的作用可以用于描述BTZ黑洞的量子化，也可以用于研究chen Simons理论。一个玩具M理论将基于一个特定的N=1 Virasaro作用来研究。

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.