RUI: Supersymmetric gauge theory and Dirichlet-branes

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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