An Algebraic Approach to M/Superstring Theory and Supergravity

提议的研究是用代数方法来理解M/超弦理论和超引力的各个方面。PI提出在不同时空背景下获得M/超弦理论的谱。主要目的是在这些背景下更好地理解AdS/CFT的二元性。PI打算进一步研究测量N=2超重力理论，并了解它们在M/超弦理论中的嵌入。本文将探讨共形超群的超相干态基与谐波超空间之间的联系，以期理解AdS/CFT对偶性。在一个更正式的领域，PI将研究扩展超引力理论的非紧致对称群的幺正表示，并利用这些信息更好地理解M/超弦理论。

The proposed research is on algebraic approaches to understanding aspects of M/Superstring Theory and Supergravity. The PI proposes to obtain the spectra of M/Superstring theory in different space-time backgrounds. The main thrust will be to understand better AdS/CFT dualities in these backgrounds. The PI intends to make further studies of gauged N=2 supergravity theory and to understand their embeddings in M/superstring theory. The connection between supercoherent state bases of conformal supergroups and harmonic superspace will be investigated with an eye for understanding AdS/CFT dualities. In a more formal area, the PI will investigate the unitary representations of non-compact symmetry groups of extended supergravity theories and use this information to better understand M/superstring theory.