RUI: Supersymmetric gauge theory and Dirichlet-branes

本文利用IIA型弦理论/ m理论、IIB型弦理论/超引力和Dijkgraaf-Vafa矩阵模型的结果，重点研究了超对称规范理论的非微扰性质。本文主要研究了10维超引力理论中存在的3维和6维空间膜（膜）的性质。为了更彻底地理解非平凡引力和b场背景下的dirichlet膜，PI提出在某些二维N = 2超共形协集模型（Kazama-Suzuki）背景下表征d膜的谱，并在某些已知等效为体理论的模型对的边界态之间建立同构。PI还建议确定与某些四维N = 2超对称规范理论相对应的精确m理论构型，并使用这些理论来计算这些理论的预势的非微扰修正。PI还计划采用矩阵模型技术来研究上述四维N = 2超对称规范理论的非摄动方面。在鲍登大学的本科生参与研究方面，PI取得了巨大的成功。作为研究的一部分，他将指导本科生对二维杨-米尔斯理论（一种精确可解模型）的研究

This proposal focuses on the nonperturbative properties of supersymmetric gauge theories using results from type IIA string theory/M-theory, IIB string theory/supergravity, and Dijkgraaf-Vafa matrix models. The research focuses on the property of 3 and 6 space dimensional branes (membranes) that exist in 10 dimensional Supergravity theories. In order to more thoroughly understand Dirichlet-branes in nontrivial gravitational and B-field backgrounds, the PI proposes to characterize the spectrum of D-branes in certain two-dimensional N = 2 superconformal coset model (Kazama-Suzuki) backgrounds, and to establish an isomorphism between the boundary states of certain pairs of models known to be equivalent as bulk theories. The PI also proposes to identify the precise M-theory configurations that correspond to certain four-dimensional N = 2 supersymmetric gauge theories and to use these to compute nonperturbative corrections to the prepotentials of those theories. The PI also plans to employ matrix model techniques to study nonperturbative aspects of the four-dimensional N = 2 supersymmetric gauge theories described above. The PI has had great success in involving undergraduate students at Bowdoin in research. As part of his research, he will supervise investigations of two-dimensional Yang-Mills theory, an exactly solvable model, with undergraduate students