D-Brane Physics and Calabi-Yau Geometry

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DMS-0301476David R. Morrison, Paul Aspinwall, and M. Ronen Plesser.String theory is one of the most challenging and interesting fields inboth mathematics and physics. Widely considered the most promisingapproach to formulating a complete unified model of physics at themost fundamental level, it has also spawned many ideas in puremathematics. The original idea of string theory was that all fundamental constituents of the universe were open or closed loops of string. It has become increasingly clear that this formulation of the theory is incomplete in essential ways. One of the missing pieces is the phenomenon known as "D-branes", which naively appear to be geometric objects of variousdimensions: points, strings, membranes, and so on, which coexist with the fundamental strings of the theory.A satisfactory mathematical framework for studying these D-branes, and an understanding of their physical nature, are lacking. In this project,mathematical techniques from algebra and geometry will be used to uncoverthe concepts required for a precise definition of these D-branes. Theresearchers will develop new mathematical tools, as needed, as well asapply existing mathematical tools to attack this problem. The physical nature of D-branes in non-trivial backgrounds will also be investigated in detail, using methods from quantum field theory and insights from supergravity. The insights gained from the study of D-branes will be applied back to the physics of gauge theory and string theory, as well.