RUI: Supersymmetric gauge theory and Dirichlet-branes

这个建议的重点是超对称规范理论的非微扰性质，使用的结果从IIA型弦理论/M-理论，IIB型弦理论/超引力，和Dijkgraaf-Vafa矩阵模型。研究了存在于10维超引力理论中的3维和6维膜的性质。为了更深入地理解非平凡引力场和B场背景下的狄利克雷膜，PI提出在某些二维N = 2超共形陪集模型（Kazama-Suzuki）背景下刻画D膜的谱，并在某些已知等价于体理论的模型对的边界态之间建立同构。PI还提议识别与某些四维N = 2超对称规范理论相对应的精确M理论配置，并使用这些配置来计算对这些理论的前势的非微扰修正。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微扰方面。 PI在Bowdoin的本科生参与研究方面取得了巨大成功。作为研究的一部分，他将与本科生一起监督二维杨-米尔斯理论（一种完全可解的模型）的调查

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